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.