Just as a point of clarification, the Cl- couldn't attack the carbon until the H2O left because there isn't a hydrogen on that carbon. It is true that Cl- is a weak nucleophile, but this substrate was specifically chosen so there wouldn't be competing SN1/SN2 reactions, only SN1 is possible.
Also, if you look at the E1 elimination sequence, you would start with the carbocation, H2O, and Cl-. If the Cl- pulls off a proton, you will have the alkene, H2O, and HCl. Now consider what happens to alkenes in the presence of strong acids and see what you get from that reaction.