I'm having a little trouble picturing how a batter who has just hit the ball and is entitled to run to first base, but just stands there in the batter's box, is "doing what he's supposed to be doing".
The old "tangle play" is well documented in baseball (and in some softball rule sets). That play specifically covers a batted ball that is in the vicinity of the plate, as on a bunt, such that the batter exiting the (right-handed) batter's box must cross in front of the catcher as the catcher must come forward to field the ball. There, both players are "doing what they're supposed to be doing"- so long as the batter is going straight toward first and the catcher is going straight for the ball. In that one special case, both interference and obstruction can be ignored. But, if either pauses, or deviates from that unavoidable "straight-line" path, interference or obstruction can be a viable call.
There might be elements of this play I'd like to see in person to get a better idea of exactly who did what. If the batter just stood there, with plenty of time to vacate the area, in my mind he's doing what he shouldn't be doing and he's opened himself up to an obstruction call.