I see no evidence whatsoever that the pilot ever said why he wanted lower. For all the controller knew, he wanted lower for favourable winds, and when he has other conflicting traffic, a "standby" is an entirely appropriate response to such a request.
If the pilot had, instead, said "I need lower due to pressurization failure", now the controller has a reason to give priority handling, even absent the dreaded e-word.
Sure he did:
"Nine Hundred Kilo November, we need to descend to about 180," the pilot informed the controller, sounding coherent and calm. "We have an indication that’s not correct in the plane."