I was friends with a guy who's girlfriend would never watch him bowl or play basketball.....he ended up inviting me along
I'm a singer, and if I have a gig somewhere, I would be hurt if my husband wouldn't go listen to me. He plays basketball, and at first, I'd go every time he played...but I was the only woman there

so I quit going. I just supported him by telling him to have fun, and kissing him goodbye before he left, and then I'd tell him, "You'd better win every game for me!" and he'd say, "I'll try!" Then, when he got home, I'd ask him if he won, and sometimes he'd give details of some of the plays. Even though I didn't fully understand, sometimes, I would listen intently. Eventually, I got the hang of Basketball rules...I could never play though
It sounds like he wants you to go watch him play tennis, because the other players' significant other is there, and he's embarassed that his doesn't seem to care enough about him to do the same for him.
As for playing video games, it sounds like that's a bit selfish of him to expect you to sit there and watch him win a game he's mastered, for the thousandth time.....I think he thinks it might impress you.
Or maybe, he's had a girlfriend before that would gush over how wonderful he is because he can play the game so well, and now that you don't gush over how marvelous he is, he doesn't feel as good about himself.
Sounds like a self esteem issue on his part...it's not exactly realistic to expect your partner to be there for EVERYTHING you do. Sometimes, there are certain things you don't have in common.