Nice catch. I happened to be home that day, and was listening to my feed (I had just noticed a big weather cell go through, and tuned in to see what might be going on). I caught about the last half of the conversation that you posted, and when the controller turned him over to the KVNY tower, I went looking for the KVNY feed, but it was down.
I tried the link to the KVNY landing portion that you posted but it gave me the error "something is wrong".
I see from Flightaware that he obviously landed safely and continued his journey, but during this episode you could hear the tension in his voice when he was talking to the controller. It has to be pretty scary to be flying through that kind of weather with a malfunctioning engine. I'm sure that was an event he won't soon forget.
Your KBUR feeder