Well, I was going to say that it's just behind the Rec.
There was the base of a winding drum there, which (if I'm reading an old map correctly) hauled waste from Whitworth Pit up the mountain. My Grandpa and I used to walk up there with our jam sandwiches for a picnic in the summer holidays when I was about 7 or 8 years old.
Anyway, I don't think that's the one in the picture - I don't remember the quarry face in the background.
I can remember that when Ty Trist was still open there was an aerial device, with buckets, from Tytrist to Troedrhigwair, dropping the spoil from the pit onto the mountain. Could this remains be part of that mechanism?