No, people don't usually say that, because it is obvious to most people what the product is in that situation, and trying to redefine terms so that it's something else seems like newspeak.

The game is a product — the company produces it. The players are players — they play the game. The whales are a sub-category of players, so if the players are indeed the product, you'd have to say they're buying themselves. In fact, the game is a product that both paying and non-paying customers consume, in some cases with barely differing experiences.