(presumably some silences are trimmed here as they often are in these videos)
The initial and somewhat generously subtitled request to return at 0:35 was missed by the controller (switching frequencies?) but so was the somewhat more clearly expressed one (but not PAN/mayday) at 0:50.
The thing that stood out for me aside from the absence of a PAN/mayday call (assuming nothing was missed by the scanner as has been known to happen) was the number of times that both parties said something (request/directive) which seemed to require a prompt response/readback from the other but then continued with additional information/direction which led to transmissions crossing. This got quite dicey at 1:30 when the emergency aircraft stepped on tower's attempt to route company out of their way and assumed the heading was for them.