Their business model is undoubtedly ads. But I think that's slightly different from saying they are an ad company. As far as I can tell, the primary reason that Google exists is for clever technical people to do new geeky stuff. They need a way to fund that geeky stuff and that's where ads come in, but the ads and the revenue aren't where their real passion seems to be. If they could simply sit back and watch the $$ rolling in through ads without ever doing another bit of innovation, I doubt they would do it.
This is quite different from the vast majority of companies. BP, for example, don't exist because their peope are passionate about drilling oil - it's because drilling oil is a very good way of making money. Even companies like MicroSoft exist (and pretty much always existed) primarily as a money-making business. Sure they attract lots of nerds, but the money driven the company's choices of where to deploy those nerds.