Trump certainly does lack the legitimacy steaming from the popular vote win, while still being legally elected per archaic but still existing stystem.
The popular vote is meaningless when it comes to legitimacy, and more meaningless than ever given California's bizarre system that drove down GOP turnout massively.
The popular vote is meaningless when it comes to who legally gets elected President, but not to legitimacy. Losing the popular vote by over 3 million is not a ringing endorsement by the public as a whole. Republican turnout wasn't down in California, they just refused to vote for Trump, which is evidenced by seven Republican members of Congress being re-elected even though their districts voted for Clinton.