I've just restored the 4 hinges of my 71 and some had similar play. As Tom said, you should be good.
in worse case scenario if the hole has turned oval, you need mark the center for later reference. weld/fill the hole
and after some grinding redrill it using the reference marks pointing to the center. No biggy, there's plenty meat on the original hinges.
Some detail I did that you may need do as well, on 1 hinge, the distance from the metal of the part that pivots was much greater than
twice the thickness of the bronze top lip provided in the kits, which would have allowed too much vertical play, needed to be corrected.
In the vice, it was 2 secs of work to fix. Basically all they needed was a massage to restore the parallelism, easy to be checked with a rod going thru the 4 holes.
Keep in mind that if one hinge has play, chances that the other has some as well are very high (even if when still on the car you do not really feel some due to weight and angle). Considering the patina I see on your vid, I would not even think and just replace all 4. You would hate yourself to have to do this once the car is all aligned and painted etc... :O