@ [MENTION=2092360].Volsung. Didn't DnD restrict things like what classes could use what? Or is that somehow not an RPG? If you ask me, though, role-playing is about the character you play, not the equipment he or she uses.
There are some silly restrictions in AD&D (2.0) like clerics not being able to use piercing weapons, and so on. This doesn't exist in 3E, instead you have to learn feats to be able to use weapons proficiently. That doesn't stop you from creating a sword wielding wizard or a staff-master warrior.
As you say equipment is not what defines the genre. But the genre is defined by the freedom to act according to variable choices, and about the world responding accordingly to these variations. If our choices are taken away, the game loses part of its defining elements. So role-playing is about "how you play a character", not THE character. In every single game we play as a character, even abstract game-playing characters as in the case of Tetris.