That latter definition is in fact a reasonable counter-argument to Windows being a monopoly (people did buy Macs), and that's why Microsoft got in trouble for the deals they cut to try and crush Netscape, not for making a more popular OS than Apple did.

You can't define a monopoly as "your competitors aren't popular" because otherwise it'd be illegal to invent new product categories, as at the start you'd be the only player in the new space. You can't define it that way for another reason: it punishes success.