I've often wondered what I'd rule if a similar play happened in one of my games. It matters less to me now that it was my son's playoff game, but I'm always trying to learn and have data to help just in case it does happen to me!
Interesting - judging "intent" throws a curious wrinkle into other interference type situations, but is not in the words of the rule (1-21-1a - "...an act (physical or verbal) by the team at bat which interferes with, obstructs, impedes, hinders, or confuses any fielder attempting to make a play...").
On this play, batter knows the ball went down and knows his offensive situation. He was attempting a bunt with a runner on first & second. So that runner either is going to second or need to retreat to first if he misses. All pretty normal stuff. Now I have to decide whether the batter knowing he missed the ball in the dirt intended to make a right hand turn just in case the catcher tries to throw to first so perhaps the umpire will not make an interference call because he judges I didn't intend to get in the way. The batter could/should have very easily looked around to find the ball as well and decide which way to go so as to not possibly get in the way. On other wild pitch or passed ball situations batters routinely look around to find the ball to tell the runner(s) to go to the next base. I guess there's part of me that just believes it's still the batters responsibility to make sure he doesn't get in the way.
Consider the play where there is a wild pitch with R1 on the move on the pitch. Coach tells runner to keep coming to 3rd base. Batter has backed up out of the box, only watching runner (he's excited as that's the winning run), catcher retrieves ball, throws ball, hits batter. You still don't have interference here? That run could score now depending on where the ball goes. It's not all that different of a play as the batter was out of the box, not intending to interfere, but yet he impeded the catcher's attempt to make a play.