Linux games give Ubuntu versions in the system requirements, and I know that they will also install to and run on down-stream distros based on Ubuntu, such as Linux Mint and KDE Neon. My question: Do they also work upstream, on Debian? Or does it depend on Ubuntu features that don't exist in Debian by default?

They'll probably work, but Support won't help you to get them working if they don't. You should still be covered by the thirty-day refund option though.

They work on any distro but names of required packages might differ or not be easily available on some. These Ubuntu are the only ones GOG tests games on.

I've played lots of GOG's linux offerings on Debian. Whether stuff will work really depends on what versions of packages the games in question are linked against. Sometimes they're stated on the game page, but usually not

Also, GOG tells developers to package for Ubuntu 18.04, so stuff is either out of date, or developers just ignore GOG's instructions, or they simply don't provide the Linux binary at all.

Just think of Debian as stale bread, as Ubuntu as stale croutons, and Mint as the breadcrumbs that are fed to the birds.

To continue with your analogy, GOG's beloved 'Bionic Beaver' is expired bread

I recommend looking at play.it
The package has scripts to install games that have been tested on Debian.

Yeah, maybe they should just get a Steam Desk and aim at Arch for a minimum viable target.

I find that all linux games I run work well, I use OpenSUSE.
If you install Lutris you can use that to auto configure windows games for you, I find it works well.

Can't speak for Debian, but haven't had any (much) problems with Fedora. My brother has had luck with Solus as well (but wouldn't recommend that distro until they've sorted their faff out).