It's quite simple, it's not democratic in the sense that the majority of the population voted for another candidate, but in the end Trump got elected.
Final ballot count:
Hilary: 65,844,610 votes
Trump: 62,979,636 votes
Now, I understand these are the electoral rules in the USA and I'm not saying Trump won unfairly, but he certainly didn't win democratically since the majority of voters didn't want him there.
If this starts a movement to abolish the electoral college, great, but the core problem here isn't a few million votes. Even with a different system Trump could still have won. The core problem is that such a guy was able to even get close to the White House and the root cause is a dire failure of all the other politicians to address the concerns he addressed.
Arguably executive orders should not exist, nor should a powerful President. The Swiss system of a rapidly rotating presidency and strong "state rights" seems preferable to me. But the USA has strong elected Presidents and I never saw any American seriously challenge that setup, I hear more talk of states seceding than I see talk of changing the constitution to limit the power of the POTUS.
So I don't see your point. The people were given a (fairly crappy) choice, made it, now their preferences are being implemented. That's democracy.
Don't get me wrong. I think locking people who live in America out of the country because they happened to be on vacation at the time is outrageous, stunningly stupid. But maybe if prior generations of politicians had been more responsive to anti-Muslim sentiment things wouldn't have got so extreme now.