Road Redemption is the rather cool looking spiritual successor to Road Rash (an old love of mine), and it looks like it may come to Linux sometime soon.
Linux was always planned for RR since their Kickstarter, but sadly it has taken longer than we had hoped to see it on Linux. The developer did say back in August they wanted it on Linux by "Fall 2015", so looks like they may be keeping to that after all!
On SteamDB they have begun to add Linux information which points to a port being tested now:
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About the game
Lead your motorcycle gang on an epic journey across the country in this brutal driving combat adventure.
Earn money by completing races, assassinations, robberies, and other challenges in your path. As you collect loot, you'll upgrade your character, your bike, and your weapons.
One Life To Live
Driving a motorcycle at 100 mph while trying to hit someone with a pipe is dangerous, and death can come quickly. There are no extra lives nor continues. Fortunately, every time you die, all the experience you've collected can be used to upgrade your character, your bike, and your weapons.
In the multiplayer mode, you can work with your friends or fight against them. It's up to you.
You can find Road Redemption on Steam, but don't buy it until it's officially out guys.