I'm soldering my first shortwave radio kit. I've got to soldering the headers which will take the 2.5" touchscreen display. I know this may be obvious, but best to check, is the middle and right terminal in the photo not solderable? They don't seam to have the copper for solder to attach to. I assume that the kit just doesn't require these connections to the display?
From what I can see from the picture there is no copper in the via, just soldermask. So as indicated in the comments, either the PCB stackup is incorrect or you placed the component on the wrong side of the board.
Regardless, these should definitely be plated through like an ordinary via, so the PCB is incorrectly designed/manufactured. And they should not be round vias but ideally oblong similar to the shape of the leg. There should be as much metal to metal connection as possible, professional soldering does not involve large air gaps.