There issue is not that she doesn't like it (though I'll come back to that in a second). Everyone has different tastes. But that she says, to quote the OP: "She thought videogame music isn't sophisticated enough to match old classical music, and I'm sure most people would say not much of any other music is."
The issue is "sophisticated enough." This is where Janet Levy's "Covert and Casual Values" is useful. When people say "sophisticated" or "complicated" they mean sophisticated or complicated harmonically. They are using as a universal value to judge all music one criteria--developmental harmonic complexity--which was primarily the concern of a group German composers from 1750-1900. The judgement then says, French classical music isn't as good because its harmony isn't sophisticated enough. And of course popular music or film music can't be as good because its harmony isn't sophisticated enough.
But there are musical values other than complicated harmony. The blues, as a genre, uses only 3 chords. That's it. By the values that says Beethoven is the best composer ever, that this girlfriend seems to hold, no blues ever can be good music. The Blues isn't interested in complex harmony. It is interested in complex timbre. Jazz is interested in complex improvisation. There are genres interested in complex rhythm. And others interested in complex melody or complex ornamentation. Still others value simplicity rather than complexity.
I like art music, but I don't dismiss other music from being good because it doesn't match the values of art music.
This is like listening to a folk singer and saying that folk singer sucks because they don't sing like an opera singer. No duh, the folk singer isn't trying to sing like an opera singer.
Now on to the second issue. Sure, listen to the music you like. But (and this is were "Anything but Heavy Metal" is useful) genres often carry meaning beyond their sounds.
On the first day of my classes, as a way to illustrate this, I often ask my students "What kind of music do you like?" I often hear, "I like all music, but not country." Of course, when I press them, it turns out that a) they don't actually like all music and b) they don't really know anything about country music--they wouldn't know Patsy Cline from Taylor Swift. With further questioning, these kids often like folk music...or they say they do. They often say they like the blues as well, maybe even bluegrass. I then play some songs in these different genres...that are the exact same song, often sounding the same as well (Maybe "John Henry"). What's the difference if it isn't the sound? When we talk about it, it turns out, most of the time, its because they associate country with conservatism and a part of the country they don't like and they don't want anyone to think they are conservative. In short, they want people to think of them a certain way, so they say, "I don't like country."
Similarly, I point out that never, in all my years of teaching, has any student ever said to me, "I like all music, but not classical."--even though I'm pretty sure there are many students in class who don't like classical music. But there is anxiety that if you *say* you don't like classical music, people will think you are uncultured. On the flipside, people who say things like "I like classical music and don't like any popular music," tend to be broadcasting a lot more than just their musical taste.