Making your own door, Take 2

He even looks up at the ceiling, like maybe something went wrong up THERE somehow

That's not the reason. We have push/pull to allow more efficient flow of people and prevent accidents. The reason why it broke was because he pushed too fast.

I wonder if he didn't just get confused. Like, he KNEW the door could be opened either way, but he was in a hurry. Faced with a time-hindering decision and in desperate need of some lunch, his brain panicked. Now his hand is reaching out to pull the door, but his body decided to push. The end result is he shoulder-check's the door into non-existence. On the plus side, the handle did survive.

It appears to me that the door is only a Pull door, you can see the placing of the base and the hinges, it doesn't swing inwards as the hinges prevent that. It even has one of those things you put at the top to slow the door down when it closes, those usually only go on oneway doors. If the door could swing in, it wouldn't shatter regardless of the speed he was running or the pressure he placed on it.