Romp means to run or play happily or boisterously.
away there has the locative sense, departing, moving farther and farther from a place.
P.S. away can also mean to do something continuously without interruption, to be engaged in doing something.
He snored away.
She puttered away in her pottery shed.
He strummed away on a banjo while the infant in its crib cried itself to sleep.
A romp is an easy victory.
They romped over the other team.
But nowadays we (speakers of AmE) don't say "the football team romped away". Your dictionary is in error there if it defines "romp away" as "to win quickly and easily" in contemporary American English, where it was used 100 years ago, when college students were wearing raccoon coats.