Zulu,
I thought the same exact thing on first seeing the photo, but after looking closer it’s clear that the two cable ends go through the handles/dolphins from the outside then up between them where they’re attached to the chain.
It still seems kind of unusual that they would use the dolphins as a stop like that (to keep the cable from sliding back on the barrel), and it appears like there’s absolutely no padding on the cable (or rope?). It also strikes me as odd that the barrel is lifted with all the weight bearing on one spot instead of having two cables, or slings as I’ve seen used in many other instances of a barrel being raised. I wonder if the people hired to retrieve the barrels were commercial salvagers as opposed to ‘marine archaeologists’?