In that definition, the surrender of part of the browser window to advertisement is the "valuable consideration". It's only worth tiny fractions of a cent, sure, but heap those fractions up high enough and it becomes worthwhile.

For your position (that ad-supported implies searcher is not the customer) to be correct, there would have to be some minimum amount of cost involved before a human can become a customer. Say the search engine charges one dollar per query. The searcher must be the customer, obviously. What if the search engine charges one a penny per query? Is the searcher still the customer? What about one thousandth? One millionth?

At what point does the searcher's expenditure fall so low that you consider them to be a product, rather than a human?

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Aside:

Apart from my day job, I write a lot of software. Some of it is made available for use for no monetary charge, and supported by ads. I do not consider the humans who use my software to be "products", nor the advertisement networks to be "customers". To say that someone is a product just because they don't want to pay money for something strikes me as borderline sociopathic.