Yes, but Trump can run for one more term as follows.
Trump wins re-election.
On last day of first term he resigns, and Pence becomes president for one day.
Since he didn’t complete a term, when he steps into office he then is beginning his first term.
Then he can run again.
Or they could keep on playing the same game.
Twenty-Second Amendment
"Section 1. No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of President more than once. ..."