The latest game powered by CryEngine that "intend[s] to support Linux" is Cradle from Mojo Game Studios. Cradle is a Kickstarter-based game that is an open-world adventure in a fantasy setting and features action and exploration.
Some time ago Phoronix had exclusively reported on CryEngine 3 having a Linux port and now it looks like it will finally be taken advantage of by several Linux game titles in the near year or two.
Cradle is part of an active Kickstarter campaign that has currently raised $72k USD of a $350k goal and there's just eighteen days left. More details on this game that intends to support Linux can be found via its Kickstarter page.