You don't need to go to a different site to play with the puzzle/game. It can be done right from the ad.
Note that the advertising may have nothing to do with puzzles/games, but the interactive puzzles/games draw you in for a while so that you notice the ad more.
So now creating an effective ad involves not just creating the ad itself but also the puzzle(s)/game(s) that will go along with it.
Personally I avoid clicking on anything ad-like, to avoid pop-ups and generally having the flow of my web browsing interrupted.
Now, if the execution was really good, with a nice design and a fun-looking gameplay, that may change. The gameplay should look intriguing even before the user clicks on the ad -- maybe show a demo screen, like the arcade games?