Word of God (Miyamoto) is that they're more of a theater troupe than anything else. Bowser is the Designated Villain in these cases, which is why he still gets to race karts and play golf with the peeps. There was also this one comic which depicted this.
Oooh, I too hope this is going Super Crown. Also there are lots of explanations for his interest in Peach (though I like the idea she's a literal toadstool). The simplest is that he just wants her kingdom like so many villains. The cutest is that it's just another game to them like tennis.
The only way this makes sense is if Peach isn't a mammal (Bowser EMPHATICALLY has romantic, and presumably sexual, interest in her), and if Peach isn't a mammal, she's probably a fungus, and that would make Bowser's complaint at the end even weirder.
