The sling swivel thingy is for a cuff sling that attaches to the bottom rail of a vintage .22 match rifle and adjusts to the position on the rail where you want it. Likely a Parker-Hale/Bisley unit for a BSA or some such depending on the size of the "square" that slides along the inside of the rail.
When you have it where you want it you can then detach the cuff sling from it and not have to readjust it. I've a couple of them fitted to different match .22s. Easily the most valuable thing in the pile if you clean it up and it's marked.
Just above it is the rear sling attachment plate for a Mossberg .22. A 1.25" swivel with a locking T fits into it. Insert the swivel, turn, and it locks in place. They were used on many vintage Mossberg .22s like the 42 M-B trainers.