Probably just need a seal kit, but if you take the cylinder off the loader and extend it out fully, you can check the rod and see if it is damaged. If no damage then reseal it, otherwise you may have to replace the rod too.
Pretty sure that a LA1153 loader would be too big for a B7800 tractor. It was simply a picture used as an example and it's not the actual loader of the tractor.Candidly, from the look of that loader, I'd almost bet the pins are sloppy too. East to tell how much slop there is. Before you mount the loader to the tractor and it's standing on it's built in removal legs, try wiggling the uprights back and forth. If the move excessively, the pins are worn.
I just replaced all the pins on the loader on my one M9, but I machined my own in the shop from bar stock. They are pretty expensive to purchase and only a dealer part, no aftermarket.