Right now the only (supposedly) viable competitor is Facebook, but it's more of an advertising duopoly that divides the market - all the people I know who advertise say that you use FB for brand/interaction/marketing and Google for sales, and for a specific spend it is usually clear which one gets it (and seldom if ever anyone other than FB or Google).
I am a Google customer. They provide me with a product (Google) which I pay for by allowing Google to display advertisements on the results.
A business is also a Google customer. They pay Google to display ads to a visitors to the website.
But that distinction is moot anyway. Businesses aren't covered by consumer protections because they aren't "consumers".
You're really a user; not a customer. Customers pay. Google is selling your eyeballs to advertisers. Advertises are Google's customers.
And the important distinction if you want to counter the argument that the person you're replying to is making:
Customers pay with money. "paying" with a currency like privacy or convenience isn't actually paying. If you aren't paying for something with money you aren't a customer, you're a user.
Rest assured that if you were a google customer, the IRS would want their pound of flesh from that barter exchange you and google are having.
It seems Google's primary competitive advantage is a well-architected technology platform (though Steve Yegge may disagree) and the world's top talent. But there's nothing like the kind of total control over critical infrastructure that the Bell System had which is the definition of natural monopoly.
That was eventually overturned in court, but it was a decade-long fight. It took another decade before third parties were allowed to sell devices that transmitted sound through the phone system with acoustic coupling, and another decade after that before you could just plug in your own phone.
For everything Google does, there are viable competitors. They may not be nearly as large, but they're extremely easy to switch to if you want. People don't stick with Google because they have no choice (as would be the case with a monopoly) but because they like it more.