It's a funny one. He's trying to deny parliament a vote in order to make something the public voted for happen, as the public is a larger group, they're the priority. Personally, I'd say that's in support of democracy if not slightly grey. Parliament has had, what is it now? 3 years? They've got nowhere, they're not getting anywhere in the space of 2 months. Just more yapping on about another referendum, leaving the EU without actually leaving and some Scottish yobbo proclaiming that Brexit means an independent Scotland (Good luck when the EU won't take you in because you don't meet their requirements and we're not propping up your economy and ageing population)
This may well be a case of a necessary evil for the greater good. Only time will tell.
As for the "unelected" remark. Much like May, Boris was elected. When we vote for a political party, we vote for just that, a party. The party (usually) chooses who should be the face of their party. Boris was voted in by the tories, the tories were voted in by the public. Therefore Boris was elected. If you stopped playing identity politics you wouldn't be so blind as to how our own Government system works in regards to elections.