Well actually... he still won the election, according to the rules and regulations in place at the time (which applied to both Trump and Hillary equally).

Thus what HraVelho says is correct: he is deemed to have been elected President of the United States of America, by the American people.

I don't like it anymore than you do (at least I suspect you don't like it)... but the great thing about the American way, as HraVelho said: there are new elections every 4 years!

If however, things break down to a point, in which after each election, one side tries to impeach the other side, or attempts to remove the president without waiting their turn to the next election...

then the greatness of the American way will have been lost.

ESSENTIALLY...

we can't go through life expecting that only the candidate we like, and the one we voted for, will win. There will be presidents we don't like. (In fact, now that I mention it... I haven't really ever liked any of the Presidents! Is this the best our civilization can do?!)

So again, if we don't like a President, then we've got to wait our turn at another shot, in the next election.