That clip is one of the "normal clips" for the later type trim that is used in the middle of the trims. On at least the some ends of the trim the clips are different with a square metal clip that is tightened by a nut on the back to hold the trim firmly on. In the trim itself you should see some cutouts in the lips where the square piece slides into the trim before you tighten it. Pretty sure the one on the front of the doors and the final one for the rear panel trim are teh square metal ones.
Good luck with the plastic ones, as most are brittle by now and although not broken, will break when trying to remove the clips.
Do you need the door trim for a 4 or 2 dr.... 4dr should be much easier to get and I should have one of those if you need it