Ovinomancer
No flips for you!
Well, yes, which is why I said acting is sufficient but not necessary to roleplay.Roleplaying is not acting, though acting is roleplaying.
However, "Bob the fighter swings the sword," is also not roleplaying. The person controlling is not playing the role, but rather is just dictating how he's moving his piece. It's like playing Monopoly when I say, "7! The car lands on Virginia Avenue." Had the person said, "I swing my sword," that would be the person inhabiting and playing the role with no acting involved, rather than just dictating a piece move. Similarly, I can roleplay Monopoly if I really feel like it. I just have to say something like, "7! I put myself into gear and screech off, corning around the jail and stopping at Virginia Avenue."
Nope, first person is not required to roleplay, although you may prefer it. The player saying, "Bob the Fighter swings his sword," is engaged to the role of a Fighter and declaring actions against the fictional positioning of the scene from the standpoint of that role. A token in Monopoly lacks any such role in a fiction and is just a pawn.
This isn't to say that preference for first person declarations or even acting aren't valid -- they most certainly are. Care should be taken to not lump preference into definition.