Is this door closer okay, maladjusted, or broken?
There are a few adjustment that are pretty easy to do, once you figure out which adjustment screw does what, That can be sorted out by trial and error. There should be one on the other end too. One is backcheck, which I could never figure out what it really did, and the other two are closing speed, which is good in the video, and the last one is latch speed which is supposed to slow the door down so it does not slam from the closing speed. That appears to need adjusting if anything. The door could stand silencers too (jamb mounted door bumpers).  

Oil on the hinge pins would be a nice touch too. 

To answer you question, yes it is correctable, usually with an adjustment on either one of the three screws you will see. Two of which you have pictured.