Or maybe this company that sent the takedowns, Marketly (not MS, just someone with whom they have a contract), never sent takedowns to Bing. (Why is of course open to speculation; maybe Bing isn't popular enough to be worth the effort)
That still leaves Microsoft in a position where they pay others to send takedown notices to their competitor for the stuff they don't bother to take down themselves. You'd think they'd do that for themselves, too, if they thought those links are so horrible for their own business. My guess is they just want to mess with Google and waste their time on money chasing hundreds of thousands of links a month.
Man, you need to pay more attention to Hanlon's Razor. What's actually happened is Microsoft's xbox division has paid this company to do something about xbox piracy. And this company has sent takedowns (legitimate, I might add) to google, not out of some dastardly plan to waste google's time, but to try and make it harder to find pirated xbox games. The juiciest angle supported by the facts is "third-party Microsoft supplier thinks google more useful than bing", and while that's not exactly flattering to microsoft, it tells us nothing we didn't already know.