In my opinion the problem here largely lies with the controller not providing more information on where he was trying to position Cathay in the first place, and then continuing with the instruction when it was clear there was a risk of loss of separation.
That is, when he gave the first turn instruction he should have advised CPA 892 that the turn should be immediate to get in front of UAL 1515, and once that didn't happen, he should have lined CPA 892 behind UAL 1515. The direction to turn was quite late given the position of the aircraft in any case. I think it's very odd that he didn't change the sequence when it was clear the initial instructions were not followed and so could cause loss of separation. it seems reasonably clear that the controller was fixated on managing congestion, which he probably does his entire shift. I would say that is the root cause. Both pilots express a surrendering of control to ATC.