The application almost certainly runs. It's the anti-cheat that causes issues 99.99% of the time at this point. It relies on certain things being available in the system, and it needs special support to work on Linux (and some features won't work, like having kernel level access to read memory).

If you're using a mainstream AC solution, they've already done most of the work. It often just needs to be enabled and rebuilt with Linux support turned on. If it's custom, then there's a lot more to do.

Sometimes the game runs fine in Proton but there are a couple of small things that don’t work right. The dev could probably iron out the kinks on their end. Usually games just run fine for me.

I will say, Valve needs to fix the Steam overlay in Proton because for some reason the text is so tiny on my 1440 monitor that I literally can’t read it. Give me a UI scale option.

I managed to install a heavily modded version of Fallout 4 with Fallout London through non-steam .exe’s with Proton, so at this point I’m convinced it can handle anything.

Maybe they mean support it in the sense they will enable comparability layers for any anti cheat? I am not familiar with this game or whether they use AC or not; just giving a plausible example of what support may look like.

Also keeping your game proton compatible is still technically "supporting" it.

Sometimes updates break compatibility and I've seen devs release patches to unbork their game.

It is. I'm a bit confused by that as well.