to reign in

in that sentance, the term means to come close enough to Emily to be able to beat her in the race.

Reign in , in this situation is being used to give the vision of bringing that person closer in order to pass and win the race.

hmm, actually, it's not a race but a freestyle event so I guess the tv host is saying that Loe is trying to follow the steps of Copeland (trying to perform the same jumps) in order to start well and maybe finish on a stronger trick at the end of the run to beat her.

am I correct ?

The sentence is using the wrong "reign". "Reign" refers to soverign power. "Rein" is the leather contraption attached to a horses head by which a rider controls him; hence the proper form to use in the example.