I spoke to the developer on Twitter a few days ago to ask about Linux support and they gave a very clear "yes, soon!". They also said it should arrive once the initial release for Windows & Mac settles down.
About the game:
High Hell is a neon-soaked, arcade-action first-person shooter from Terri Vellmann (Heavy Bullets) and Doseone (Enter the Gungeon, Gang Beasts). Descend upon the criminal underground with the most blessed of shotguns and bring lethal salvation to those that have fallen from the light. Righteous fury and fancy footwork are crucial to survive an escalating, absurd series of outlandish missions. Pop brainwashed chimps, deface corporate effigies, and dismantle the business dealings of the unrepentant cartel in a vibrant remix of the classic first-person shooter.
Certainly looks like a lot of fun, certainly my kind of shooter. You will be kicking doors down, kicking ass and generally causing hell. From the gameplay and the description, it sounds like you don't actually have to run in guns blazing after kicking the door down, as there's more than one way to enter a building.
The gameplay is fast, designed for the PC with no compromises for gamepads. It's also rammed full of action, with no interactive cutscenes, just fast and twitchy FPS fun.
Looking forward to it, as it looks completely nuts.