There is plenty of recent research that shows that games are in fact great exercise for the mind.
Google it and then show it to your Mum.
Furthermore, if you really want to be a game developer when you're older then having a thorough understanding of the game industry and your personal tastes, surely would be almost mandatory wouldn't it?
Tell that to you Mum too.
I'm also planning on getting b2goty when it goes on sale next. (Hopefully I'll nab it for under $20)
From what I hear its a pretty good game but then again you can't always trust what people say.
For example I've seem plently of reviews giving mediocre games (like deus ex hr and the walking dead) 10/10 so who knows???