PlayStation was hugely enabled by Square "rebelling" against Nintendo and siding with Sony, while XBox has broken through at least partly through its fervent support for its developers.
How are you measuring dominance? I don't really follow these types of things closely, but hasn't Nintendo been in the video game business longer than any of its current competitors and hasn't the Wii dramatically outsold it's current crop of competitors? They've certainly had plenty of flops and bad years, but who exactly is more dominant than Nintendo in the console arena?
Plus, all you have to do is go back a single console generation and you have the Gamecube which was absolutely dominated in pretty much any category you can think of by the Playstation 2. Even the Xbox, a console by a company no one though should develop a console, managed to beat the Gamecube in sales.
Go back one generation further and again the Playstation dominated the Nintendo 64.
I would argue that Nintendo hasn't been in a dominant position in a very long time. The sales of the Wii were a big win for Nintendo, but they aren't really delivering on the games front. The Wii was sold at a time when the casual market was ready to explode. But now it's just turned into that thing no one uses. Hell, I bought a $99 Wii for my girlfriend's parents mainly so they would be able to watch Netflix. Sure, it was another Wii sale, but that's not exactly what we usually talk about when we talk about dominance in the gaming industry.
You may not have bought a lot of Wii games, but they are competitive on the tie ratio metric: http://www.vgchartz.com/analysis/platform_totals/Tie-Ratio/G... Basically, on every objective metric, they are either competitive or flat-out won this round.
It takes a lot of dancing to try to claim otherwise, but a lot of people seem ready to do that dance. I'm not sure why. I don't like Apple particularly well personally, but I don't try to run around proving they aren't an extremely successful company.
Oh, and if we're going to talk console dominance, one should probably not forget that Nintendo has simply owned the portable gaming world for 12 years now, since the Gameboy came out. The only thing that has ever successfully competed with the Gameboy or DS lines are the next Nintendo model.