I'm not sure if it's so much that KC knows how to win games as it is that they have that "aura" now. We watched this so many years w/ the Pats - other teams make the crucial mistakes at the end of games. There is almost an intimidation factor there, where teams can almost feel the sense of deja vu and it gets in their head.
That's certainly true when we play KC in the playoffs now.
2 games in, I don't think KC is any better than the Bills are. If they are, it's marginal. It's the psychological hurdle we have to get over.