No Crysis Wars client is available for Linux and this server release does depend upon the Windows game files, but if you're interested it's now available. We don't anticipate seeing a Crysis Wars / Crysis Warhead Linux client either considering the game's engine uses a DirectX 10 (with version 9.0 fall-back) renderer and we haven't seen any other Crytek game clients published for Linux.
The announcement along with the link to this first release of the Linux server for Crysis Wars can be read at Icculus.org. Ryan has yet to provide any update on the Linux Prey client with either the retail binary that's still not been released or an updated demo. We also have no idea on when Ryan Gordon will release the Unreal Tournament 3 Linux client, which is quickly approaching its one-year anniversary.