Things like alcohol, tobacco, addictive drugs in general, gambling, sex, shopping, and video games - all these things *DO* chemically alter your brain!
Not because they add external chemicals to your brain (though some of them obviously do) but because they stimulate the release of neurotransmitters. All the activities I mentioned (and, as far as I know, anything that can be addictive) can activate reward centers in the brain. This can lead to addiction - your brain grows used to the release of these neurotransmitters, in their absence you crave their presence, etc...
While video games obviously don't inject chemicals into the body, they can stimulate the release of, for example, dopamine in the ventral tegmental area. Just because it comes from within your body doesn't mean it can't get you addicted.
Yes, I play video games. Yes, I'm a neuroscientist. No, this isn't my specific field, so don't take anything I say as particularly authoritative - I may well have gotten some things wrong.