After talking to the man, seek the gambler and talk to him. Now, you have to play a game of poker inside the bar and win the gambler's money back. You have to bust out all the three opponents to unlock the achievement (Poker Bully) and to get the gambler's money back. You can do this by playing at Novice level. Talk to gambler outside to retrieve the necklace.
Next, head outside town and find the drunk. Kill him and loot the watch from his body. Then, head to the next target. Kill them all then loot the body to get the item. Return to the quest giver to complete the mission.