Why does the spec only say Windows 10/11? Is this not a DosBox game? It should work on just about anything!

Probably because GOG no longer provides support for Windows versions older than Windows 10. That does not mean games don't work on other operating systems, just that GOG may not be able to help you if you encounter problems trying to use the games on operating system that is not listed.

Yeah, they appear to have gotten a bit lazy here... I'm fighting with trying to get it to run under Linux - Lutris simply says there is no launcher. I'm trying a manual install via wine, and at least have part 1 working... I don't see how to get part 2 working at all (apparently not a dosbox port?)

It's an Apple 2 game.

So, download an Apple 2 emulator and use it to run Phantasie 2. Or, you could see if AppleWin is included in the install (it might be), and then just run it under WINE and load Phantasie 2 under it. I know for a fact that AppleWin works under WINE.

MAME can also emulate the Apple 2. (I used it to play Nox Archaist.) Drawback is that it can be harder to set up, but on the other hand, it avoids one layer of "emulation".

(Note: Might be a good idea to back up the disk images, as any time the game saves, it will write to one of the (virtual) disks.)