a video game is basically you playing as a character to achieve certain goals depending on the story, gameplay mechanic, etc. basically, you don't play as you, you are playing in the role (or in control) of some other character(s) (be it link, master chief, a bunch of protoss zealots, stick-man in a flash game, etc). in this way, EVERY video game IS role playing (the earliest such were MUD's and text-based games where one dark corner can end up with you getting devoured by something, lol). the only reason we now have such diverse game genres is that the basic context has branched out to a thousand different ways (if you ever played contact, you'd know what i mean). if you're blasting someone's face full of lead, it's a shooter, if you're bashing some guys head in with a hadouken, it's a fighting game, etc. but you're still not playing as you. you're just in a mostly predetermined role, playing a game.
add to that the fact that the latest zelda (in the DS, anyway) had options to change equipment (boomerang, whip, bomb, bow and arrow etc), your outfit (you have to unlock them, though), your health (find hearts for link, get a complete set of upgrades for the train) and even had side quests (gimme a ride there, deliver x number of y item here, even one where you pick up the photographer near those hellish trains) it is easily a pseudo-RPG in terms of genre (it's mostly classified as an action-RPG)
PS
there, you got me started, muahaha. peace. and i hope the guy does find some game where our equine friends are given their due, though i think it unlikely.
EDIT: ok, maybe not EVERY video game (what role would you be playing in tetris, for example, lolz) but certainly90+++% of them