I would say that's not normal. You're supposed to get much better battery life than an iPhone, but yours is much worse. I couldn't find battery life for the Touch, but here's the iPhone 1st gen:
Are you getting 6 hours music + 1 hour games + plus 1/2 an hour video from one charge or are they 3 separate charge tests? Your usage would depend on what format and bitrate your music files are encoded at, what settings you used, where wifi or EQ on etc, what games you were playing simple 2D or complex 3D, your video size and quality etc.
To get a more accurate idea of your battery state I would suggest you shut everything down you can, wifi, EQ, screen brightness, etc and do an uninterrupted single media test and see how long you get just playing music.
Maybe you're keeping the screen on constantly while listening to music? I discovered this and stopped, and I noticed extreme improvement in my battery life. Make sure you don't have any apps running in the background as well.
You can also follow Apple's battery maintenance. I believe it's like...fully charge (4 four hours) it then drain it completely and leave it for an hour or so then fully charge it again (4 hrs i believe). It's on their website. Tell us how this goes :]
Maybe you're keeping the screen on constantly while listening to music? I discovered this and stopped, and I noticed extreme improvement in my battery life. Make sure you don't have any apps running in the background as well.