Post-Game Routine

JMO, but it there's pain or significant soreness then ice. Otherwise it depends on the individual.
Generally icing should happen soon after pitching rather than waiting for that night. I like to see some sprints a while after icing just to get the blood flowing again but there are people who don't agree with that. A protein shake soon after completing his outing followed by a good meal that evening is probably a good idea. I prefer rest the next day, a lot of people like to see some light throwing to get blood flowing to the area and to keep the arm from tightening up. After that number of pitches or more I like to see 2 days without any hard throwing and then a pretty good long toss session or bullpen if the arm is up to it, followed by a day off or light throwing and then a bullpen followed by another day off or light throwing before the next start.

Lots of different approaches out there.

There are a lot of different approaches.

Personally, I like to see pitchers do a light post game stretch for their upper and lower body just as they would at the end of any workout. This might also include running a couple of poles in the outfield.

For nutrition, it's important to get a good meal after a game, but added focus should be put on hydration as well.

Stu

Nolan Ryan was infamous for riding the stationary bike for 20 minutes after each of his games. cool downs are just as important as warmups are.
I would do a light cardio workout like jogging on a treadmill. stretch. I also found it a great time to do core work or core stabilization workouts; light of course depending on how many pitches thrown in a game.
Most pitchers prefer getting their work done (pitching specific exercises) right after practice or a game so they make sure the do them and don't have to them at home.