I'm not sure what your definition of punishing is...you include games that are challenging/very difficult, but also games whose subject matter you find repellent and don't want to play because of this (e.g. Postal 2, Ebola).
I don't play games whose difficulty I find to be excessive.
I also don't play games whose themes I find repellent (can't think of any personal experiences right now though there probably were some)...interesting subject though where one's personal limits are. Is it morally ok to play and enjoy games like that murder simulator Manhunt or that Japanese rape game Rapelay? Would you be fine with playing a slavery or concentration camp simulation if the game mechanics were good?

Syobon Action?

As for puzzle games, Spacechem is awesome but not actually all that hard. For honest mindfucks, try DROD 5 or Stephen's Sausage Roll. For a genuinely punishing / unfair lateral thinking game, try The Fool and His Money (if the warning in the title is not enough, it also costs $40 per platform).

Ghost & Goblins

I can only imagine how many NES systems were thrown through windows because of this fucking game. :P

Probably one of those MMOs that gets people so addicted that they play until they die. Can't get much more punishing than death.

At least not until someone develops a peripheral that spits on the body afterward.

Sure I could mention some permadeath roguelike or some arcade game port on NES without saves or [url=https://www.youtube.com/watch?v=vUc4GkMN1qs)]"Domination" (from the James Bond movie "Never Say Never Again")[/url] which gives you lethal electric shocks if you fail... but instead I'll mention:

Forsaken

If you claim you have finished the PC version playing on the hardest difficulty, I say you are lying. If you don't run out of ammo before the end of the level, then you will run out of time and lose the whole game.

Each Forsaken level is timed, you have to find the exit before the timer runs out, but most "rooms" within the level are designed so that you can't just speed through them. No, you have to kill all enemies in each room before you can continue to the next room.

And since ammo is so scarce, if you try to shoot them fast, you will miss more, meaning you run out of ammo, meaning somethingsomething.

I Wanna be the guy !
Have fun !!! ^^

"The game provides players with a choice in terms of their deathrate"

OH, we have to get this here! :D

I ran out of ammo on Normal. The only way I could finish the game was to play on Easy.

Hellfire on the Genesis is really punishing. It's a horizontal scrolling shooter. Die once, and you'll have to reset the game since you lose all of your powerups and you need them, big time.

Also, The Immortal.

That game isn't really that punishing. When you get killed (which will happen a lot thanks to all the hidden death traps in the game), all that happens is that you are sent back to the last checkpoint with your lives reduced by one. Running out of lives isn't even an issue; the game will continue, with your lives counter becoming negative. See also: Eryi's Action, which is a commercially released game with a similar premise (that the game is filled with hidden death traps).

(Of course, one could treat "punishing" as meaning something different, in the sense that the game frequently punishes you for doing reasonable things.)

Anyway, here are some games that really *do* punish you:

Wizardry: The game auto-saves so you can't just reload a save (unless you back up the character disk). If your party gets wiped out, you need to make a new party to find your old party. If your party teleports into rock, time to start over. I can characterize it this way The game randomly deletes your characters under certain circumstances, and this behavior is *not* a bug.

Wizardry 2: Like Wizardry, but worse: If you lose your party, you have to start Wizardry *1* over, as Wizardry 2 expects you to have transferred a high level (13+) Wizardry 1 party.

Wizardry 4: You *can* just reload your save, but otherwise, this game is known to be evil. In particular:
* Enemy uses a strong spell on you: Will probably kill you. (On the first floor, one enemy can cast MAHALITO (4-24 damage), and you only have 10 HP.
* Enemy casts MAKANITO: For a while, if this happens, it is an instant game over. No ifs, ands, or buts, and no chance of surviving it; if the enemy decides to use that spell and gets it off before it kills you, *game over*, and time to reload your last save.
* Certain spell casting items randomly break when used, and some are plot-critical. Also, some enemies can steal any item you don't have equipped. (Fortunately, if you lose an important item, you can get it back where you originally found it.)
* Past the point of no return without a certain item? I am afraid the game is now unwinnable, and you must load a save from before that point. (You did keep a save from back then, right?) To its credit, Wizardry 4 does provide a clear warning right before the point of no return, including a hint that you might need something. (Interestingly enough, one clue about how to get that something comes *after* the point of no return.)

I could probably mention La Mulana as another punishing game: whip upgrades are lost forever if you fail their puzzle (though the remake provides a way to reset the puzzle), the puzzles can be rather obtuse, and the game frequently punishes you with lightning for doing reasonable things like checking for breakable blocks.

By the way, if you want something lighter, the English GBA version of Final Fantasy 5 has a character who likes to "pun"-ish you. Also, I think Undertale might do a bit of this (plus a regular punishment if you choose to kill everyone). IWBTG uses a lot of material copyrighted by other well-known developers (including Nintendo, Konami, and Capcom), and therefore isn't the sort of game that could be sold in a store like GOG. In fact, I don't think GOG would want to host it as a free download because of the copyright issues.

On the other hand, Eryi's Action, which doesn't infringe on the copyright of others, could be sold here if the developer chose to.

Ports of Call (when played by me)

North & South (when played against me)

Rick Dangerous (when played)

Well excuse me General Longstreet!

Regarding the difficulty, I found "Dungeon rats" (available here on Gog) to be pretty extreme.
It's a turn based combat game, with some of the hardest fights I've ever seen in a computer game. I did manage to beat it on the hardest difficulty once, but stopped a second playthrough when I got stuck on a fight (updates had changed some things since my 1st playthrough...possibly removed some bugs I might have benefited from the first time :-)

Can't you at least reimport the winning Wizardry 1 party if you die in 2?

I haven't played the original, but the remake is rather fair with lightning. If there's an eye in the room, hitting the slab (but not regular walls) will get you zapped. IIRC there's only one slab that needs to be struck, and it's in a room without an eye.

Yeah, and Super Ghouls & Ghosts for SNES is more of the same too.

I'm not sure why Postal 2 is on the OP's list. I have never played it but I've watched Let's Play videos of it and it's not punishing at all.

Other punishing games:

Ninja Gaiden 1 for NES: I could never beat the final boss because he transforms like two or three times and gets full life each time, meanwhile you only have one single life bar. That whole game is extremely hard all the way up to him too.

TMNT 1 for NES: As far as I can tell, it is literally impossible to make it through a final section of the last level without cheating with a Game Genie device. You are boxed into a super tight corridor that makes it impossible to jump or to dodge, and you have to fight a series of flying creatures that will crash into you and take away your hit points no matter what you do (you can't dodge them, and you can't kill them with attacks before they hit you either).

Wizards & Warriors for NES (although it's on other platforms too): This is an extremely difficult game, but yet not impossible to progress through like Ghosts n' Goblins and Super Ghouls 'n Ghosts are (or at least they are virtually impossible if not technically impossible).

Castlevania 3 for NES: Like with Ninja Gaiden 1, I could never beat the final boss, because he has multiple forms and he gets a new, full life bar each time, yet you do not.

Karnov for NES: You play this huge hulking guy, yet he dies in two hits like a wimp. LOL.

Robocop for NES: Another game that is virtually impossible if not technically impossible.

Contra III for SNES: Yet another game that is virtually impossible if not technically impossible. On one level you have to hang on to the bottom of a helicopter while tons of enemies swarm you. You have only a couple of millimeters in which to move. If you try to dodge the enemies or bullets, you have to jump...but if you jump, there is 95% chance that your jump will either cause you to fall off the helicopter and die, or jump into any of the several dozens of enemies and bullets flying towards you and die. And you don't jump, then either the enemies touch you or their bullets touch you, and either way, you still die.

Friday the 13th for NES: The things the player needs to do to progress this game are obscure and make no sense. By default, the player has no idea what he or she is supposed to do because the game does nothing to explain it. In recent years, youtubers have disclosed that information and afterwards tons of keyboard jockies made claims like "This game is easy, I beat it in the 1980's." I think those keyboard jockies are lying. IMO no one knew how to beat that game (with maybe very few exceptions) until the youtubers told them how to do so in in this decade.

Abadox for NES: This game is brutally hard all the way through. I could never beat the final couple of levels without cheating with a Game Genie.

Blaster Master for NES: Very difficult although the player can learn how to progress via trial and error.

Battletoads for NES: I'm not sure why this game has so much acclaim since its unplayable due to extremely bad play control mechanics in certain sections that make it virtually impossible. I.e. The part where you have to avoid crashing into rock pillars is virtually impossible without a joystick, because with a controller's d-pad you'd have to switch between pressing "up" and "down" way more quickly than the d-pad can reasonably accommodate. Likewise, the part where you are tied to a unicycle and have to out-race the giant balls of death that kill you instantly in one hit are awful because the play control while turning corners is abysmal and therefore forces you to lose speed. When a player dies due to these things it's not because they played badly; it's just because the play control is horrendous.