From a post on Steam, it seems Linux support could become a thing in the future, which I hope. The developer didn't say a word about it since more than a year ago, but maybe things will change, now that 1.0 has been reached...

If you don't want to wait for a native Linux version, the game works perfectly with Wine. I made an installer script for Lutris: https://lutris.net/games/banners-of-ruin/ (currently still unpublished and waiting for approval).