Crysis Wars has native Linux version of its dedicated server, but it's only 32-bit and no existing SSM works with it because all SSMs have Windows DLL, so it's not very useful. However, as you know there's Wine project that allows you to run Windows apps on Linux and other systems. It works quite well with Crysis. Not only dedicated server, but even the game works there. With some sneaky tricks i get almost same FPS as on Windows. That's quite impressive.
Few weeks ago i bought Linux VPS from Hetzner to host Crysis server on it. Right now, the "something" server lives there and as you can see it works. The original Crysis dedicated server is not so nice because of that damn ineffective console window. It's basically GUI application, so it requires GUI to live in. Having GUI on server is possible, but it's just useless waste of server resources. This is one reason why Windows Server is so bad, because it has the GUI always. To fix this issue i made another custom Crysis dedicated server launcher that doesn't have that console window. You can find it here
https://github.com/ccomrade/c1-headless. It acts as simple console application (no GUI), so it can be easily started as background service.
So, yes, running Crysis server on Linux is possible. There are still some things to do and even Crysis server itself is far from perfect, but it works. For example, my server automatically goes to next map even when nobody is playing there, so it does map change like 10 times every day. The problem is that every map change slightly increases memory usage of the server because of some memory leaks in Crysis code. After few days without restart it eats noticeably more memory, so it needs restart time to time. Also, automatic server restart after crash or something works well thanks nice service management in Linux, so you don't have to mess with some batch files (worst scripting language in the world by the way).
I want to run ctaoistrach's server on the VPS as well. He has own custom SSM called nCX with interesting features, but its code requires small clean up. Sadly, nCX seems to be the only SSM that is still under active development. The VPS probably has enough power to run more than 2 Crysis servers, so if you or anyone else has some nice Crysis server with unique features, i can run it there too. Maybe it will attract more new players, so we will finally have more highly active players than servers. :D