Having a hobby is healthy as long as it doesn't dominate other areas that are more important. Spouse, kids, work, health, - These should always take priority. Hobbies are a welcome distraction from all other responsibilities in life. However there are times a hobby can become a distraction. We all know people who do something too much. I'm sure you know people who: watch too much TV, Surf the internet too much, play on their phone too much, play video games too much... Etc. See what I'm getting at? Try to look at it from her side. Is it dominating time you should be investing elsewhere?
I work long hours (60-70 hours/week). I decided that I would avoid hobbies that require time away from my family. So, if I'm not working then I'm home. I can play 15-30 minutes and it isn't a big deal since it is at home. My kids and wife can play too if they want. However, if there are things I should be doing more (cleaning, reading to kids, making dinner, etc) then I do that first. Otherwise you should look at your priorities.
I bought a game my wife liked (WOZ). We have found some overlap in games we like but not all of them. I have many friends who's spouse never plays their games. This is fine but it is more fun to share interests if possible.
What does your wife enjoy doing?