[dmsfrr]

Yes the stud is supposed to be part of the arm at the bottom of the seat-back. It looks like the original weld on the outer flat side may not have been sufficient, allowing it to fall out.
Pull the vinyl boot off of the arm and you should see the empty hole where the stud fits in. Put the stud all the way back in with a clamp or two keeping it tight and give it a quicky welding job. That should fix it.

If you need a picture of either side of the lower arm and stud without the vinyl cover, I've got another seat-back here that's out of the car and fairly easy to get to.
Example photo is of the passenger side...
.