That does look like it could be it, there on the machine. It has leather straps, which the Jacket Doctor's watch had, and unlike the watch in the guy's bedroom, this one has a round face, which the Jacket Doctor's also appeared to have. In fact, it looks like the machine is carrying several similar watches.

Looking at Hungry Earth now ... how could he have gotten the watch off Rory though? It would have vanished with him, no?

Okay, you get a good clear look at Rory's watch the instant after Amy gives him the ring and leaves, there's a shot of it between Amy's arm and body as she turns away. It also looks like the one the Jacket Doctor wears. I'm not convinced it's the same one he had on the oar ... there's a dark gold trim around the face.

Checked Cold Blood, and he's still wearing it when he gets shot.

At any rate, the appearance of several watches that look like the one the Jacket Doctor wears is looking good for the theory!