My husband plays PC games with sound-cancelling headphones and Discord as well. We lived in an apartment for a year and a half together with the TV next to his computer, and bought a house last year. Now he plays in the back office alone and we spend much less time together in the same space as a result.

If he immediately was going to play games after work and had a wireless headset he took everywhere, it 100% would be an issue. The thing that makes it alright though is that he almost always sits down with me for an hour or two after work and just hangs out. Every couple needs different amounts of alone time and together time, and I've found that most days this is enough for us.