Well, Adsense / Analytics is another. Google can track you across the internet, and offer that information to search query bidders. If you don't want to bother spending money advertising to people who read HN, it's achievable. Less so for say, Bing or Yahoo. Being able to target better than other platforms alters your willingness to pay to advertise there vs elsewhere.
I suspect they also have a better grasp of the value of traffic acquisition. They pay a lot of web related tech firms to use their search engine over competitor's. We know the only time they lost a bid for Firefox's search placement was when a former Google executive was working for a competitor. It's not clear whether Marissa brought Yahoo some better insight into the value, or if she just needed to accept a higher risk of overpaying for traffic.
But what stops an aggregator from offering to put your ad on multiple search engines, so you pay for clicks from Google and whatever other search engines people are using? There may not currently be a lot of extra clicks available that way, but it's more than nothing, and you'd benefit from whatever improved competition might come up, and incidentally give it more resources to improve with and to cut Google's margins to your further benefit.
AFAIK this isn't happening, but why? Is there another moat I don't know of?