Not sure that I understand the question, so please excuse me if I'm misunderstanding it.. I don't think that chuck will fit on a deluxe headstock due to the larger spindle bore. That looks like a smaller bore headstock to me. I'm not sure if anyone makes one that will fit on the deluxe or not. Maybe someone else has more info on that.
What I do know is That It is an independent chuck as opposed to self centering. An independent chuck can have It's advantages depending on what You want to do with it, but most cue lathes use a self centering chuck. when tuned in properly They are quicker and easier for the average person to use as they automatically center the workpiece. They use a scroll, and all jaws close in conjunction with each other at the same time. On a independent chuck they are manually adjusted one jaw at a time. That could come in useful when you need to mill a piece while It's off centered, or could possibly give more adjust-ability during the centering of a piece, without the need for shims, as with a self centering jaw you are pretty much stuck where It centers without any independent/manual adjustments other then the shims.
As an every day chuck I like the self centering, but I have run into situations when the independent adjustments would be very useful to me.