Mike Meginnis turns out to be the perfect person to answer this question, because he's not only interested in video games and video game theory, such as that exists, but he's also a writer. (I'd categorize him as a rational aesthete.) He sent me the below thoughts in an email.
So, re: first-person games versus third-person games, I think there are a lot of things. First and foremost, 1st-person games are nothing like being inside the body of the character. Your peripheral vision is shit, you move like a jet-fueled unicycle, and there's this gun constantly hovering just below eye level. The only remotely fun-to-watch FPS I've ever seen is the Metroid Prime series, I think partly because suddenly this stuff has an explanation. You're wearing a helmet with a visor. You can see your own reflection (Samus' reflection) sometimes in the visor. You're pretty much a tank, really, and so the gun's constant hovering makes sense. It's immersive in a way that Halo can't be. And of course the speed of a competitive FPS is terribly disorienting. You spend most of them basically spinning.
But I think also it has to do with drama. Say you're doing a jump in Halo. What are you jumping toward? How close are you? And how close are you now? These questions are extremely difficult to answer. Depth perception in 3D games is awful -- this is why Mario, in 3D games, always has a shadow. Without it, even in the third person, jumps are nearly impossible. but at least in the third person you can have the shadow! In first person you don't even see your feet land on the ground. You know you made the jump if you're not falling. It's imprecise, which hurts playability, but good players get around it. Watching, however, becomes much less fun when there's a lack of precision, because if you aren't in control it's very hard to get a good feel for what's going on.
On the other hand, a jump in Mario is a beautiful little story. You're jumping toward a coin box. Your guy hits the coin box. A coin comes out. It makes the coin sound. You fall to earth. Probably you do this again. It's never unclear what's happening, what the stakes are, or how close you are to succeeding. If you fail -- or if the player you're watching fails -- it's not ambiguous how it happened.
I also suspect it's easier to identify with a body from outside than from inside. I find my own body rather mysterious. Sometimes I look at my limbs and I think how weird and long they are. I think the problem with being someone is you know how little's going on in there, or in any case you have a strong sense of it. You know it doesn't feel like anything to be Master Chief, or to be yourself. (Or anyway, I don't feel like much of anything when I'm me.) But to have an object for your identification -- to imagine what it's like to be Mario -- is really involving. My feeling is that internal lives are something we project on each other more than something we really experience. (What we experience, I suspect, is largely a result of knowing others are projecting on us.) Think of the hollowness in most second-person narration. It's right there at the center. And, weirdly, that hollowness is you. In a very literal sense, it's you.
Or something like that. Basically it comes down to the fact that people are more compelling to watch than they are to be, I think.
I love this last idea. A long time ago I read that most people dream in the third person. I dream in the first person, but, oddly, I often replay memories in the third person. Same goes for when I imagine myself doing something in the future or an alternate reality, as if the point of the exercise were to see how it would look if I did something, rather than how it would feel.