I think the issue is conscious versus unconscious thought. Baseball has a lot of conscious thought, but not much unconscious thought, which involves far more complex information processing than conscious thought.
Baseball requires more analysis and conscious decision making based on those analytics. Hockey requires far more complex real time decision making. In baseball, managers and stat geeks will look at how the outfield needs to be positioned for a batter or even pitch to pitch, and the pitcher and catcher have to figure out pitch selection, but most of that is slow and conscious decision making. Hockey- positioning yourself on the ice, calculating the velocity and angle of other players, both teammates and opponents, predicting what decisions they're going to make, picking out where and how to pass or shoot, all in real time? It's not conscious decision making like baseball demands, so you don't perceive just how much thinking you're actually doing, but you're actually processing orders of magnitude more information when you're playing hockey. The only part of baseball where you're engaging your brain at a similar level is reading a pitch and hitting it. That's obviously a really important part of the game, but only one player has to do that at a time, and they'll do it for 5 at bats a game, averaging around 25 pitches. That level of information processing is demanded for about 30 seconds a player per game. Hockey players have to do it continually when they're on the ice, and process many more variables than just bat and ball. And everything happens really, really fast. So each player is putting in an average of 15 minutes of really intense mental activity. Basketball has similar dynamics, but often happens at a mild jog, 4 mph. Hockey, everything his happening at 40 mph.
Football is a little weird. Some players have their memorized play and they execute or not with little room for improvisation and reaction, others require a whole hell of a lot of both conscious and unconscious choices. Being a Quarterback is probably the most mentally demanding position in sports. Hockey players are thinking about 12 trajectories and how to react to them, a quarterback is thinking about 22. Being a lineman? You have to memorize and execute. That involves substantial memory, but very little mental processing.