I suspect they had some extra fuel on board, very lucky for them or the news story could have been somewhat different.
Airliners ALWAYS have "some extra fuel on board"! They have reserves, alternate fuel, and sometimes a bit more than that.
IIRC, they landed about 18 minutes late, which would not have burned but half their reserves, since they were in cruise at high altitude. If the autopilot was in LNAV and the arrival and approach had been entered into the FMS, the airplane would have followed that path over the ground, but constrained by altitude. The last Missed Approach heading or hold would be the final path to follow. If the route to alternate had also been entered, that is another possibility for the path after the missed approach, if the discontinuity had been closed.