Okay, I've spent a little while trying to get Alpha 21 working under Wine, to no avail. It seems related to the libcef upgrade we did in Alpha 20. So far I've tried a fair number of things to get it working (Including patches of Wine and Stonehearth...) For those interested I ended up here looking at Steam's libcef issues under Wine. There are also a ton of other games surfacing similar issues and I tried fixes for those games from various forums but I haven't hit on the solution.
I can't promise I'll find the solution for Alpha 20 and above, but you can still play Alpha 19. An easy way to get Alpha 19 for steam users is to switch to the legacy_vista branch under the betas tab for Stonehearth on Steam.
Please let me know if you are able to run Alpha 20 or above, I think the information would be valuable to a lot of other players.