1) You don't play Skyrim in 1080p on your Xbox. If you could somehow get the hardware to run that, you'd get like 3FPS. You're playing in scaled resolution. In other words, it doesn't look nearly as good as true 1080p and it isn't 1080p at all.
2) PC gaming is not expensive.
Ok, so i play on 360, and thank you. 360 is component HD, not true HD. Things look better than using the RCA (and oh my god do I hate my RCA) but just because your TV is 1080 doesn't mean you are putting out 1080. *To clarify, when I say RCA here, I'm referring to your standard A/V cable with vidoe and stereo sound. I know Component HD uses RCA connectors. I also found that I was wrong, Component HD does produce HD signals, just not usually 1080p. The 360 does not support 1080p, but it does support 1080i, so not quite the best, but pretty freaking close.*
As far as PC gaming goes, it kind of can be if you want a good build. You can get a decent PC for 800 bucks if you build it yourself (which is as easy as lego's), but an upgrade to the processor, graphics card, and sound card is gonna cost you maybe 100-150 bucks. Then you got to get the sound system, and who wants to play this game without a killer set of speakers, I know I don't (but I use nice set of headphones anyway, so a little bit off a mute point for me). So you drop anther 95 to 125 bucks on speakers or headphones. Great, you're up and running. Except you can't see that rabit out in the distance on the tiny, non-HD screen. "I can't hunt like this" you say to yourself. Time to get a 42-inch HD flat screen. 500 bucks. All said and done, you could easily drop 2000-2500 dollars on a killer gaming machine.
Do you need it, not at all. But it's possible. So now that I have blown everythign way out of purportion and left you scratching your head (though I hope you cracked a smile as well) I bid you good day, sir.