Interestingly enough for the plot of the show, it does not seem to be the watch that Jack wore in Season One. That was a Rolex Datejust, and a web-only miniepisode established that it was a gift from his father, Christian, on his wedding day.
By Season Three, he was no longer wearing it. I assumed the Others took it from him when the locked him in the Hydra Island tank and he never got it back.
Since things seem to have changed in this new timeline, perhaps Christian Shepard never gave the Rolex to his son, or perhaps Jack's father issues have lessened to the point that he doesn't feel compelled to wear that watch all the time.
Or, perhaps I'm just reading too much into it, and they needed a more legible watch for the scene.