It's just text - two bytes are good enough to indentify up to 65536 different Wii games (and there won't be that many) and another byte each for days, hours, minutes and seconds. If time is all they count, then it's six bytes per game? Not bad. You'd have to play 171 games for it to even take up 1 kB.
Though it would exclude offline Wiis, it might be a good idea to store this kind of info online. Good for Nintendo's sake, if they can access it, Big Brother-esque as that may be. They could see what games people are spending time on. If they release a game that's estimated at 50 hours and people spend 1000 hours on it, they can assume it's incredibly replayable. If they find that, no matter how long a game actually is, if no one in the world ever spends more than twenty minutes on it and then never plays it again, then it must be a crappy game.