Google isn't expecting to win any endgame with gmail. They're already monetizing it and as a consequence, it is profitable already and has been for quite some time.
You just literally stated what the end game was: monetize all uses of email, everywhere.
Remember what Google's overarching goal is supposed to be? "Organize the world's information," IIRC, with the subtext of "... and monetize it." This is literally what gmail is to email.
Google has not driven out all competitors with GMail. They have a (very) comfortable business in GMail with a plurality not even a majority of the market.
