Hey man, only one of those two smaller plastic loops needs to attach to the lower dash assembly, right at the opening, and the larger one attaches to the actual glove box like you said, and that’s it.
You will see the snap-in damper retainer pin right at the opening, it looks just like the one on the box, and the rest of the cylinder just sticks up in there, with only one of the small loops attached right at the opening. The damper has 2 small loops on the housing to allow for adjustment, but you only attach one. Choose which one works better for how you want it to open and close, and you’re good.
It will typically be the first one/ lower one, closest to the actuating arm that gets attached. No need to worry about attaching the one that goes up in there deeper, there is no other/ inside retainer pin for that one.