Great games, huh? I mean, great selection. Had the chance to play these thoroughly? :)

darkest dungeon,undertale,enter the gundeon,stardew valley,secrets of grindea,adventures of shuggy,dungeon keep 1

My favorites to play on the rare occasion that I listen to podcasts are simple games like Roguelikes (and certain roguelites) where turning off the music & sound -- if there even is any -- doesn't really affect the game's playability. Examples of games I've played this way include: NetHack, Dungeon Crawl: Stone Soup, Spelunky (I've only played the original, but the remake would probably work, too), Din's Curse (though it does have some sound cues that tip you off when monsters and other dangerous things are nearby, so...maybe not the best idea to turn off the sound), Banished, Tales of Maj'Eyal, Eador: Genesis, King of Dragon Pass (though it would be a bit of a shame to miss the music), Hotline Miami.
EDIT: "favorites [...] are", not "favorites [...] is" You mean back in the distant past of one year ago? :P

Games you don't have to think too hard, I might recommend Sonic the Hedgehog, Hotline Miami, Persona 3 and why not some Quake 3 deathmatches.

How bout Final Fantasy Tactics, you do have to think but there is a lot of time for listening aswell.

So was Judas, but he kept his original account. He just got a blue upgrade for it ;-)

Stardew Valley, maybe? You mentioned Prison Architect; I'd think building games in general (e.g. Sim City) would make good podcast games. I like to play JRPGs as podcast games because instead of "time to grind for an hour" it becomes "time to listen to a podcast, and also grind while I'm doing that," which is more palatable; but it sounds like you're looking for PC games, which I guess rules most of them out.

Depends. What's the podcast about? Am I listening to a radio show about how to cook beef? Or is it an audio book of Stephen Hawking's Quantum Mechanics? The brain can only allocate so much to multi-tasking efforts before stress and mental exhaustion set in.

And yeah, the play style for me usually focuses on the words and text boxes as shapes after things become more recognizable, if that makes any sense. Text and word information gets quickly sorted by identification and rapid decisions. For instance, I usually play games like Rimworld and Prison Architect on fast speed, even with music or a podcast going on in the background. My brain is rapidly absorbing information, making choices, and doing lots of click click click and hitting hot keys. It sounds stressful, but in its own weird way it's relaxing.

Then again, sometimes it's just fun to crank up some Slayer, load up Doom and enjoy the fun with your brain set on snooze.

At the complete opposite of console-gameplay, there's Euro Truck Simulator 2 which is the best way to listen to radio streamings and podcasts. The gameplay of ETS2 could appear as slow but like in real life you need 100% attention otherwise you end up crashing into things ^o^ The big plus of the game is that radio streaming and mp3 player is natively implemented and you can easily add your own radio stations (if you know the URL stream) or music/podcats.

I don't know how big the demo of ETS2 is but if it's as generous as the demo of American Truck, you're already in for at least a dozen hours of gameplay and can definitely check if it's your dope or not....
http://store.steampowered.com/app/227300/
And if you're a true Polish, you can add the national eagle on your truck while listening to Radio Eska :o)
http://store.steampowered.com/app/304020/

Ugh, the only games I could play while listening to something else would be games like Solitaire or Minesweeper. Maybe Mah-jongg.

Other suggestions would be timer-less puzzle games like TIM.

I wouldn't really recommend 4X games like Civ, MoO or MoM even if you know the gameplay by heart, because in the end game it's easy to overlook something important like setting production or enemies creeping up. Early game might be okayish, because the basic building is always the same.

Another option would be real time builder games like Settlers, Cultures, Banished. Those usually have a lot of idle time while you watch things being built. And you can always pause the podcast when you get into a tight spot (like warfare).

Portal sounds like it may fit, it's a gem, and fairly easy going, sometimes not so easy going. Though recommending a valve game to a gog mod seems entirely ridiculous.

World of Goo, you do have to pay some attention to your goo balls though.

Evil Genius, because always Evil Genius. That also applies to Startopia.

Oh right, Hexcells would be a safe bet in that case.

Personally I like roguelites like Risk of Rain and Ascendant for listening to podcasts.