Is Video Game Music Actually Music?

I was discussing music with somebody earlier today, and I was talking about an old style of music that I thought was flat and really had no variety and that it was really hard for me to consider as being music.

This person replied that it's no stranger than thinking video game music was really music.

Here is this person's definition of video game music: a tin tin tinny sound created by a synthesizer that can't be called music, because it's created by a computer and not a musician. Not only that, but all video game music basically sounds the same.

Now this person is by no means a gamer, but I was still shocked that she thought that. (This person is usually open-minded about everything.) Yet here she was, claiming that video game not only wasn't music at all, but that it was common knowledge that it's not.

What do you think about this? Is the fact that it's created by a synthesizer (usually) automatically mean it's not music, simply because it's not created by actual musical instruments nor performed by an actual musician?

I need to organize my laptop, make sure everything is as it should be, and take care of a few other things to make my life normal. Then I'll see about being active.