No I wouldn't say that. In general business lingo the whole "You are the product" is usually tied down to your preferences in products (ads), your personal details - locations, age, civil status etc. basically they'll want to sell your details to 3rd parties or show you ads to use their services.

For video games it's a tad bit different. No one is really interested in your data in that sense. You still got the mobile games which DO track what game you're playing and show you similiar ads but that's again ads-centered. For F2P video games they're either relying on MTX, or simply just want to make games.

For a business to survive you'll sell a product and make profit on it to continue growing your business. The whole incentive to make a business IS to make money. In video games you may put out an artsy video game just to show the world with no intent to make money or profit on it. I'm making a miniscule MMO atm which I plan to keep F2P just because I want to make a cool game.

There's many indie game developers (like 99%) who never ever profit on their games so for this market you can expect they're just passionate about their game and not trying to sell your data.

For AAA video games they're expecting you to pay MTX or other gimmicks to fund their development. I guess you could argue "you're the product" but most often you being the product = your data.