You're saying the vehicle will bring all the fuel needed for a return flight to Earth down to the surface of Mars and then back up again? Do you have a link with a description of how they're going to do this?

No. It will make the fuel from Martian resources like water ice and the CO2 atmosphere. Using solar power. First to split the water to oxygen and hydrogen using electrolysis, then use the hydrogen with CO2 to make methane (& some water which is cycled back to the electrolysis step) using the Sabatier reaction. This is done on the International space Station today, by the way. The methane on ISS is simply vented (as the point on ISS is to recover the oxygen from the CO2, which is most of CO2’s mass). It takes a lot of energy, so there will need to be very large solar arrays on Mars, but it’s possible.

This page describes the process: https://medium.com/spaceinmylifetime/how-spacex-will-refuel-...

Call me overly cynical, but I don't see Musk getting this done in time to be back in 2031 and win the race.

Well, he’s competing against a gov entity, so his schedule slips are going to be much less than theirs.