I know it's called profit, but the money they keep goes back into the business. The ways for it to be profit in the sense of making the shareholders rich(er) are by increasing the value of the stock or by going to shareholders as a dividend. And both of those avenues are taxed.

Nope, Google has no paid out a single dividend. As long as Google thinks it can use the money to reinvest in the company and give investors a nice return from capital gains

But dividends kept should increase stock value and the government does get a nice cut when selling those, right?