From my time in the game industry, I haven't encountered too many employers that were friendly about personal projects. I was able to get an explicit exception for one of my already released games in my contract for one of the companies I worked for, but most made it clear that they expect me not to work on anything in my own time, or that it belonged to them.
Even a game that directly led to my employment at one of the companies, as they saw my game showcased at a game convention when it was a finalist in a major game competition, saw I was local, and brought me in to discuss a possible publishing deal (which turned into a job interview).
As someone who had made and released about 8 small games on my own and liked doing it as a break from my other things, it really rubbed me the wrong way, and I didn't end up releasing that game until after I was no longer working for the company and I had lost all benefit of the free marketing I had from the contest.
It's part of the reason why I haven't gone back into the game industry since I got out. I don't want to feel like I can't make anything on my own again (especially now that I'm getting into board game design and getting game designs signed with board game publishers).
My current employer's business has nothing to do with anything related to gaming whatsoever, so even if they did try to take control of my games, they'd have a hell of a time taking me to court over it, or acting like I violated any noncompete laws.