One answer is that the watch was valuable (a Rolex Daytona Gold watch, value close to $20,000). Presumably he perceived that he might need it to barter with, and indeed he uses it to pay off the boatman later in the film.
The other, more jaded answer, is product placement. Swiss Watchmaker IWC made the watch that Jeremy Renner wears in the movie - the Pilot Watch Double Chronograph Edition Top Gun. "IWC hopes that Mr. Renner’s portrayal of a thrill-seeking lifestyle of an elite agent will correlate to the brand image." (Luxury Daily)
So if IWC has the starring role, who better than competitor Rolex to feature as a prop which is stolen and used for barter? This is supposition on my part - I can find no article suggesting Rolex was involved in the placement, cannot imagine that they would want their brand used in this way, and am aware that companies rarely pay for a product placement if a competitor is also allowed to advertise in the film.
The watchophiles in both the IWC and Rolex camps are all over this movie in their forums!