Bouwmeester was guarding a guy in the mid-slot. He couldn't just abandon him completely. There's no reason why Allen shouldn't have been able to seal the near post while leaving himself in a position where he could push across to the other side. It's a fundamental that goalies execute all the time.
The initial shot was from around the bottom of the circle well outside the dot. Note that Allen's right foot is hooked outside around the net instead of being pressed up against the inside of the post, or vertical like so:
Or by sealing it against the inside of the post like so:
Allen makes the save by kicking out his right leg, which he didn't need to do as he already had the post sealed. He merely needed to let the puck hit him without moving. Kicking out his right leg creates a gap between his body and the post, while getting his right foot further out of position.
Allen kicked the puck right back to the shooter, and now he's out of position with the post unsealed. He pushes off his left foot to lunge to his right in an attempt to seal the near post leading to the above position. Note Allen's right foot is still useless. Bouwmeester is marking his guy in the slot.
Zucker takes the puck behind the net, and Allen's poor fundamentals to this point leave him with no means of recovery. Even if he could plant his right foot, it's not in a position that would allow him to move laterally across the crease. Bouwmeester starts to react.
The goal is scored a split-second later.
IMO, this is a terrible goal by Allen.