I doubt the MLB "made" Sony do anything, though they might have pitched the idea--no pun intended.
What's the leverage? Taking the license away? Why would they do that? Doesn't make any sense. Even if Sony said no to multiplatform, it's hard to see MLB cancelling The Show. I very much doubt there was any kind of "forcing" at all.
My guess would be that MLB has not been happy with management of MLB video-games from sources other than Sony's San Diego studio. Probably painful to watch other sports series rake in the money, plus it could have a real impact with future growth as more kids American kids are picking football and basketball as their favorites. As with Disney and Spider-man, the MLB probably decided they could trust Sony to maintain a quality franchise. I know that if I were running Major League Baseball, taking The Show multi-platform would be my first choice if possible. It's a smart partnership for both parties.
