CryEngine 3 is the latest version of Crytek's CryEngine, which was released in H2'2009. I have confirmation from a source this week that a Linux port does exist, which also means an OpenGL renderer. CryEngine 3 under Microsoft Windows uses a DirectX 9/10/11 renderer while this game engine has also been ported to the Sony PlayStation 3, Nintendo Wii U, and Microsoft Xbox 360 consoles.
Crytek's Crysis 2 game was developed on CryEngine 3 while more games built upon this latest engine are forthcoming from a variety of studios. Some of the other CryEngine 3 titles include Warface, Sniper: Ghost Warrior 2, Lichdom, and Codename Kingdoms. The re-make of the Nexuiz game is also expected to be done on CryEngine 3.
While it's nice that CryEngine 3 does have a Linux port in existence (I first shared this on Twitter), there is no indication at this point that there are any titles in-development that aim to have a Linux client. The engine is simply capable of running on Linux with OpenGL but that there's no projects pending. There's no guarantee that any CryEngine 3 Linux game will ever emerged, just like Blizzard's World of Warcraft unreleased Linux client, among other studios with unreleased Linux games.
Hopefully if Valve's Linux efforts (I should have more details to share later in the month) are a big success and profitable, other studios will become inclined to provide Linux ports and at that point maybe we could see CryEngine games come to Linux, but for now don't get excited about the CryEngine potential on Linux. For now though you can play Crysis 2 under Linux using Wine, but your mileage may vary (WineHQ AppDB entry).