Free (with restrictions) isn't my idea of free, its almost like it has Denuvo DRM for a free game which is ridiculous. No wonder why Destiny 2 ended up going with Blizzard's platform instead of Steam.

Sounds like Shareware/Demoware/Pesterware, where a popup on the program will remind you that you have 6 days left, and just for fun they will also disable useful features...

like saving....

Translation of update: It should totally allow offline play when you log in to your online account.

What a sensible "restriction" for offline play.

-edited to add:

Plot twist on the "update": So even what they mean by "offline play" is essentially online-only play without being logged in.

Thanks for the OP for bringing up the problem.
After the first shock of the mandatory Blizzard app, I dig a little in the forum archives and found the links for the old downloaders:

https://eu.battle.net/forums/en/bnet/topic/15161331646

The answers lists the downloaders for the main legacy games (Starcraft Anthology, Diablo 2, Diablo 2: LoD, Warcraft 3, Warcraft 3 TFT). This morning I could still save the installers through the downloaders.

This is purely for archiving purposes and the installers only substitutes inserting the CDs, one will still need a valid CD-key for the installation.

Edit:
Individual links for the game downloaders:

Starcraft Anthology:
https://eu.battle.net/download/getLegacy?product=STAR&locale=en-GB&os=WIN

Warcraft 3: Reign of Chaos:
https://eu.battle.net/download/getLegacy?product=WAR3&locale=en-GB&os=WIN

Warcraft 3: The Frozen Throne:
http://www.battle.net/download/getLegacy?product=W3XP&locale=en-GB&os=WIN

Diablo 2:
http://www.battle.net/download/getLegacy?product=D2DV&locale=en-GB&os=WIN

Diablo 2 Lord of Destruction:
http://www.battle.net/download/getLegacy?product=D2XP&locale=en-GB&os=WIN

Keep them somewhere safe and don't use them on a connected PC; we don't want the companies to see we're playing their games by using those old CDs.

LOLWUT?

Thank you so much for this.

Are you telling me the SC .exe I downloaded from https://starcraft.com/en-us/articles/20674424 is only the launcher and not the actual installer?

Yep, this crystallizes what I hate about Blizzard right now. They want DRM everything and Everything online, and no modding or changing their product so it's a pristine vanilla product, that they can eternally monetize with micro-transactions or some other form of low-cutting corporate scheme.

I dunno. I downloaded the original that I got when I registered my StarCraft key on Battle.net long before Blizzard started offering it for free.

You are welcome. ;)

Your linked SC.exe (the remastered or 1.18) first installs the Battle.net app (like GOG Galaxy or Steam) and then after logging in you can install the Starcraft Anthology. So yes, it is only a launcher.
As I know this version downloads the full remastered game (they mention 7 GBs), but only enables the remastered option if you paid for it. Blizzard thinks it is easier to maintain only one version and does so through its Battle.net app, so the the free and remastered version is combined into a new game. (The older versions cannot even be patched to 1.18.)

The version I linked earlier is the 1.15 version and does not require the Battle.net app. It is not the installer, but a downloader: after starting it asks for a folder and then downloads a 1.2 GB installer. This installer is the game.
I have not tested, but the Battle.net multiplayer may not work, because the older version number. Other than that it should be fine.

For simplicity I edited the detailed links into my earlier post.

As a last resort for those without files or in case links go down, it may be possible to cobble together a working install with the 1.16 multiplayer-only client provided by iccup (sort of a loophole since you could always install the multiplayer portion on multiple machines). Maps should be compatible between versions, not sure how much else has changed behind the scenes.

Haven't tried this myself as knowing Blizzard I made sure to back up my files before 1.18, but it's possibly an option for those not so fortunate.

Well, Blizzard is no more, it's Activision Blizzard now.