None of the video game genre boundaries is set in stone.
So the question of what makes a game an RPG is an open-ended one, leading to many more questions.
For instance, there's an old PC shooter that I liked as a kid, called Stellar 7, except you played as a land ship rather than a person, and your enemies were also ships. But otherwise, everything was exactly the same. Does the "person" element have to be there for a game to be a FPS? (Keeping in mind that the "P" in FPS refers to point of view...)
Similarly, how far can you go toward other kinds of gameplay before you leave the FPS genre? (And the converse: How far away can games from other genres move toward the FPS before they become FPSs themselves? Is the Metroid Prime series in the FPS genre now due to its primarily FPS style of gameplay, despite retaining large elements of adventure, puzzle, and platforming?
And what about the visual layout? We can agree that an FPS requires 3D or simulated 3D, but what about the GUI? Do you have to see your weapon(s) on the screen in front of you, in your hand(s) / appendage(s) for the game to be an FPS?
Qualitatively, most of us can say "I know an FPS when I see one," with good reliability. But that's because of genre overlap. To call Metroid Prime an FPS would be legitimate, but it doesn't tell the whole truth of the nature of the game. For my part, Bioshock appealed to me at first because I heard the story was great and the gameplay was novel. I heard a lot of comments to the effect that the FPS genre had finally evolved into what it has always been destined to become. And, indeed, when I played the game the other night, if I had been enthralled by the story rather than disappointed, I might have been willing to put up with all the shooting.
I don't play games for the shooting. That's true of every game that involves shooting or melee combat of any kind, including classics like Gradius III or Final Fantasy. It's just not my thing. So, most of the time, when I play a good game I am making the decision to "put up" with all the combat, because I enjoy other aspects of the gameplay. Chrono Trigger is a fine example of that; I hate the CT battle system (and the CC system too). When I first played CT, I made it half an hour into the game and then put it away for six months because the battle engine was boring me to tears. Ultimately, though, I came back because CT has a beautiful story and some awesome visuals and music. FF VI? I play that for the character stories and music. I hate random battles.
So, the FPS genre doesn't appeal to me because it has always super-emphasized a kind of gameplay that isn't fun (for me). But when the FPS genre tries to become something more than what it has been, it can attract my attention. I'm still a Metroid fan. And Bioshock sounded really good until I got exposed to a storyline that seems like it came from somebody who had just read Atlas Shrugged, then got really fucking stoned one night and said, "You know what? I fuckin' HATE Ayn Rand! But you know what I love? Shooters! Postapocalyptic shooters! With hacks and genetic engineering gone crazy, and freaky little girls! Yeah, throw some Silent Hill in there!" (Silent Hill itself being another FPS I once nearly wanted to play, because I heard good things about the story. Ultimately, I just didn't think of the storyline as all that good.)
If that answers your question. As to Oblivion itself, I've never heard of it so I couldn't say.
