It's been a long road, with the game being funded on Kickstarter way back in 2014. I personally backed them way after this towards the end of 2015 on their website directly, so I've been watching it slowly evolve.
I spoke to Alex Koshelkov, Founder & CEO Crytivo last night. They confirmed to me that the Steam Early Access release will indeed have a Linux version, which will not use their current updater (which requires a mono-complete install to work) since it will update via Steam directly which is going to be much nicer. The actual game is built from Unity, so it should be fine.
They plan to remain in Early Access for around one year to a year and a half, since there's still plenty of work to do.
Here's a video of how it runs on Linux right now during the early stages. It does seem to run quite nicely, honestly it's vastly improved since I last tried it. Keep in mind this is a work in progress game:
If you do wish to check it out now, you can grab it from the official site.