No, you don't have to buy city. Even your opponent's level 2 cities aren't very good - they might as well be laboratories; he has one terminal action in his deck! Now, laboratory is a power-five and nothing to sneeze at, but it can't be the case on this board that the dominant strategy is to spend ten turns buying - nothing - so that you can eventually have ten laboratories.
The watchtower doesn't seem to help you very much; of course, you can't anticipate your opponent going for the city pile, but even absent that, watchtower doesn't play well with apothecary. Other than that, I don't think you make many serious mistakes, but you do make a couple. Your opponent is attempting to empty the city pile, so you want the game to end quickly. You should trash your mining village turn 7 - given your hand, it's very reasonable to expect the apothecary to net you two coppers, as it wound up doing. The turn 11 platinum should be a colony. The turn 15 silver might hurt you more than it helps; it's unlikely ever to be enough money to push you over the edge to a colony and it's bad for the apothecary. I wish I could say something more concrete! I'm surprised you lost based on the initial strategies.