Some of these games are absolutely not DOS games though and no amount of semantics can change that. Grand Theft Auto: Vice City requires Windows 98 and DX9 or newer, for example, and it is available here.

edit: I see Vice City has been removed following a DMCA request!

Yeah, many of the things we consider part of what an "Operating System" provides to programs today were provided by DOS Extenders (or forwarded to something like windows if running under that).

DPMI was pretty much an "Operating System API/ABI".

What about: if the extender is provided with the game (like DOS/4GW) then it's a DOS game; if it needs to be provided by the user (like Win 3.11) it's not.