The Unreal Engine space shooter EVERSPACE is finally nearing a Linux release, they've managed to overcome some problems and "soon" it will be released under the radar.
Helium Rain is a single-player space simulation title that's due to release on Steam on August 18th, in Early Access. The game looks good and it's being built on Linux using Unreal Engine and open source tools.
EVERSPACE is still coming to Linux, but sadly it's taking a lot longer than anyone had hoped. They've been working through the issues and have given an update.
Breaking Point is an online survival game that blends survival realism with the gameplay of a modern military shooter. It was previously an Arma 3 mod, but now they're moving to Unreal Engine 4 with a Kickstarter and they plan Linux support.
POSTAL Redux is the revamp of the original Postal with improved graphics, new game modes and more. It looks like the Linux version might finally be on the way.
Another time to show support for a game to come to Linux, if you would buy it that is. The developer of Inner Voices has stated with enough support they will bring it to Linux.