You can buy a U-shaped metal sleeve in almost any finish you want that goes over the edge of the door and both knob holes. Look up "door reinforcement plate". I'd still glue and clamp up the edge of that door just to clean things up and strengthen it as much as you can, but for $15 or less this drops right on in minutes.

I was in the same boat as you with our pantry that had a keyed lock. Some kid locked it and the key was MIA, and my door looked kinda like yours after bashing the knob off. The plate covered all the damage and tightened the door up nicely.