Does it make Google an advertising company? Yes by the bottom line, no by this strategy. It just happens it's the best way to monetize what they have so far.
Analogy: would you define 1905 Einstein as a patent clerk or a scientist?
You can look at things from a distant POV with too few details just like you can look at it from a perspective that's too close, to many details. There is no method apart from using your faculties that can replace having good faculties and the ability to apply perspective.
Ok lets see it's mission is to organize the world's information and make it universally accessible and useful.
Therefore Google is an information organization company. More than search, it's also monetizing the effort of getting all the information into proprietary databases and keeping them up to date.
Google Maps, Google Places, Google Search, etc.
Then they monetize it by advertising, as well as running their own commerce - app stores and the like. And they also give businesses Analytics, Email, Docs and other Apps that they have now unified with Google+ as well as Google Checkout for payment processing.
Now Apple, Google and Amazon compete in phone OSes, payment processing platforms etc.