As a pilot, I'm completely confused by his choice to fly all the way back to Camarillo when he was much closer to John Wayne and Long Beach (the controller is equally puzzled and asks). His lack of initially declaring an emergency wastes time while the controller tries to inquire why he's turning around, and he only does so after being prompted to do so by the controller. An engine failure is a serious emergency, even in a twin, and unfortunately this pilot's actions seem to indicate he wasn't really respecting the severity of the situation (what if he lost the other engine over the water?), while sounding annoyed with ATC even though the communication problems originated with his non-standard phraseology and lack of initially declaring an emergency. I don't have my MEL yet and only he knew the exact circumstances of his emergency, but I would have played it a lot safer in that position - nursed my still good engine in by making an expedited landing at a closer airport rather than running it at a high power setting for an extended period of time, over water, where any gliding options to other airports would be extremely limited.
Still, he's the PIC.