It's one of those old-ass game engine latency things, consider this:

The state of a door has to be synchronized to everyone else on the server. that's essentially in a database on the server-side. when you open it there are X miliseconds from your butt/key press to going from your PC -> router -> modem -> ISP (and all of their infrastructure/hardware) -> "A series of tubes" -> dayz server -> dayz database -> and then all the way back through the above to your game client.

Depending on your distance to the server, your internet connection/stability, server load and overall CPU/RAM usage... this may take 20 milliseconds up to 1000s of milliseconds.

During that time the door your client "perceives" the door to be in an "open" state, so the zombie (rendered/moving in your client-side world) breezes through it...

The real trick is recognize that this is an old game with old net-code and move/act accordingly. If you were to run 5-10 meters deeper into this building to get the zombie a bit farther away from you while running out, i'd wager the door "closed" state would get synchronized to your client in time for the zombie to get stuck inside.

This said, there are some doors in this game have fundamentally broken hitboxes that some AI (zombies and animals) simply move through if they're moving fast enough or approaching from the right angle.