Don't see why that's relevant. Indeed, it reduces the quality of American democracy, but the words democracy and republic do not contradict each other.
It's relevant because you said that Bush lost.
And he did, in the sense that fewer people wanted him to become President than Al Gore. I don't think even the Republican Party disputes this fact (although considering their problem with facts...guess it wouldn't completely surprise me.) Since the question was why people wanted Bush to be President, I thought it was a good idea to point out that they were, in fact, a minority.
Of course Bush "won" in the sense that he became President.
We have a constitution, and that is the supreme law of the land, Franzl. As awful as Bush was, he won by constitutional standards, and that is that. I wouldn't be lecturing America on how "democratic" our nation is, considering your own country's history with democratically electing awful people.....
Indeed, although I think anyone with more than a peanut-sized brain would be aware that developments in the 1930s are a bit more complicated than problems with the democratic process.
Regarding the quality of American democracy today, it's pretty hard to argue that it's any better than mediocre in comparison with the rest of the developed world.
(And by the way, I happen to vote in American elections as well, although I always question whether it's worth the 2€ to send in the absentee ballot, considering the choices and results.)