well, I’d say yes, they do care, every bit as much as the fans, or more.
https://m.startribune.com/minnesota-twins-spring-training-rocco-baldelli-sonny-gray-kyle-garlick-world-baseball-classic/600253105/?clmob=y&c=n&clmob=y&c=n
“Baldelli also repeated his exhortation from last week to the pitching staff: That it's up to each individual to do what's necessary to improve, but that the ultimate goal is a team one: Winning, first and foremost.”
"That's the only reason I'm still playing this game. Winning is the only thing that matters," said Gray, 33. "Goosebumps even talking about it, because it's something I personally believe wholeheartedly. Whatever goals you may have stem from winning."