One quick "just make it work" solution might be to ship Linux binaries with the Windows version, check if you're on wine, then execute the Linux binaries via an exec syscall[1]. I'd imagine the bulk of the game is going to be assets not code so that (maybe?) wouldn't make the game too much larger.

[1]https://gist.github.com/q3k/e5952111283ea59ee78a7699919a055b