Please do not mark Windows-only files as multiplatform. I did give it a try in Wine since I had already downloaded it, but was greeted by a black screen.
Oh whoops. It should be multi-platform according to Unity, so I'll have to figure out why it's not working.
I haven't used Unity myself but I think you need to export it separately for different platforms, or at least manually enable exporting to them somewhere. It should produce different binaries for all the platforms, for example the Linux executables will have an .x86 or .x86_64 file extension I think.