Without looking I can safely say it's not a public proxy, probably tied to your device's Google Accounts session.
First of all, encrypted traffic allows circumventing content mangling middleboxes at operators. Sometimes those middleboxes are merely annoying (say Byte Mobile), sometimes outright evil (ad insertion / replacement).
Second, a faster web experience will mean more web usage in general, and that'll translate to more ad revenue for Google.
Third, faster (or cheaper) web usage is a competitive advantage. On one hand it makes Android more competitive against iOS and WP8 (and the bit players as well). On the other hand it makes Google Android more compelling than other Android versions. Not a big deal with Amazon's fork. Potentially huge if e.g. Samsung were considering a full fork.
That's a few off the top of my head. If you try, I'm sure you too can come up with more plausible explanations than "you're the product".
Without looking, you and your misplaced confidence just ended up spouting the exact opposite of the truth:
"Further, the use of the service does not require a Google account"
Whoops. Try reading the article next time before claiming as fact something that you just made up?