I just sit & watch. Occasionally I'll clap when a player other than my kid makes a great play. That's about it. I've been on the other side of the fence as a Coach for a lot of years, so I try to model my behavior based on how I wished parents acted when I was coaching.
And, correct, I don't do replay analysis after games. I just tell him "I had fun watching you play" and let him take the lead if he wants to discuss the game. The main question I always ask is "are you hungry?" Followed by "whattaya wanna eat?"
In travel ball he likes me to take video of his at bats on my IPad, so I get to be "that Dad" in that way (!)