How do you see Video Game Music?

Oh, it's definitely separable. Primarily, I enjoy VGM on its own. Sometimes, it's only because I have nostalgia for the game, though.

Personally, I've never understood the great hype about Uematsu. I liked his work in FFVI, but I was never able to get into a lot of tracks in the the other Final Fantasy games. Sure, it all works in context.. But I don't feel the magic when I listen to the albums alone, unless they awaken my nostalgia for the games.
However, I haven't listened to his work in Phantasmagoria yet. This actually my first time hearing about it.

I'm quite fond of Yasunori Mitsuda's work though, for example. While I haven't played games like Magic Pengel 2 or Tsugunai, I still love the music from those games. His non-VGM albums, like kiRite, are also fantastic.
The same goes to music by the Falcom Sound Team. While I've never played a Ys, Sorcerian, or Legend of Heroes game, I still thoroughly enjoy the music.

How ya doing, buddy?

I used to be the same way, actually. A few years ago, I was quick to label a lot of VGM as "boring" unless it had interesting vocals. Listening to Guilty Gear music changed all that, though. Being a fan of heavy metal, Daisuke Ishiwatari's work was ambrosia.
Eventually, this led to the discovery of other game music and appreciation of the "background music".

It could just be that casual listeners need to check out more of what video game music composers have to offer.

There's nowhere I can't reach.