The reason Google uses second price auctions is because first price auctions incentive constant bid changes. The stability increases the money Google makes.
edit: For more context, and ignoring the whole generalized second price auction parts, the revenue from first and second price auctions is the same. In theory with optimal bidding and the usual assumptions of auction theory papers. The difference is that in a second price auction your optimal bid is independent of the other bidders. In a first price auction your optimal bid is dependent on the expected distribution of other bidders. In theory with all the usual auction theory assumptions. In reality with online auctions this meant a lot of churn in bids and a preference for bidding more conservatively. Which isn't good for advertisers or the revenue of the company running the auction. Second price auctions mostly solve this especially if you adjust the minimum auction price (ie: reserve price) per auction.
edit2: A great way to get more money is to have advertisers think they're bidding in a second price auction while actually running something closer to a first price auction. Which is essentially what the article talks about.