Someone on Steam has a made a controller config for it. Make sure to enable Xbox controller support in big picture first.
Add this non-steam game to Steam and rename its shortcut to exactly "Project Warlock". Then it should come up.
The config works pretty well. Make sure your game bindings are reset to default.
You know, I think that might have been me. I would say it's very much imperfect right now, and I haven't had the time to go back and improve it. I also had to amend a lot of my in-game settings to get it working the way I personally liked it, so it may not work to everyone's tastes.