Being supported by ad revenue is not the same as being an ad business.
There are ad businesses out there, companies who make ads. But Google does not. They provide a platform which does raise significant revenue from serving ads but so do papers, magazines, TV channels, podcasts, and so on.
By your logic you might as well call Formula 1 racing an ad business. They make some money from ticket sales but that’s very small compared to the ad revenue.
Nice catch.