They do, but I wouldn't consider that to be the customer paying Google directly. There's a reason why people usually use the word "tax" to refer to this (and Apple's cut on their store).

I suppose buying a gift card is technically giving Google money directly, but that isn't the same thing as payment for services rendered, it's just exchanging USD for Google Play credit, which you then spend on apps. Or in other words, you get the exact same service that you do if you skip the gift card and just pay for apps at the point of sale.