The closest I figure is Rule 6.06c, batter's interference. Runner trying to score is called out for the batter's interference, if there are less than 2 outs. Batter is not out. However, you did not state the count before that pitch, so if it was strike 3, he's already out. If there were 2 outs, the batter is out regardless, so he does not get up to bat in the next inning. This is also expalined in Rule7.08g.
Although he batted the ball which was weird, it is just considered "any other movement that hinders the catcher's play."
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