Two small points. First, you can't define anything as anything, stick with your gut on that one. If you could, the word define could have no definition, and the entire concept of definitions would be invalid. Someone getting sloppy with their definitions doesn't change the generally agreed upon meaning of concepts. I can call a rock a bird, but that doesn't actually make it so. There's a pretty reasonable definition of spam at this point.

Second, the advertising on Gmail (or Yahoo mail etc) isn't an indirect benefit, it's an exceptionally direct benefit. I've gotten to use a truly great, fast, reliable email service - Gmail - for a decade, with gigabytes of storage, and all they've done is run ads on the right side that I've never once clicked on and they never get in my way. Talk about a helluva deal. You're completely correct in the fact that Gmail ads are nothing like spam.