You don't seem to be understanding - Nintendo is a strong brand in the handheld sector, Sony/Playstation in consoles and Apple/iPod in MP3 players.
They all dominate their respective sectors.
Please state which market the XBox brand dominates with such considerable margins.
I know Americans like to perceive the XBox brand as strong but the reality is it is no stronger than the likes of N-Gage here in Europe and virtually non-existant in Japan.
As well as dominating their primary markets, strong brands transcend international borders and cultures - they don't just exist in arbitrary microcosms to suit their proponents.