Yep, it’s the mounting point here. As someone pointed out below, the insert that holds the screw has ripped out of the plastic. The base of the laptop was already broken, so put extra pressure on this part.
I’m going to strip everything out and epoxy the inserts back in place, then epoxy over the bottom part of the hinge once the screws are in. The laptop should never need to be opened again, so a bit of overkill won’t hurt here.
I’m going to try to loosen the hinge slightly too, but it looks like a pin design rather than a screw, so it might just be a case of cleaning and lubing it instead.