'Playing around with food' means touching and moving around the food in your plate without actually bringing it to your mouth.It's usually done when someone isn't hungry or doesn't really like what he's eating (children especially) or else as a sign of nervousness.
In this case,it is probably being done to prolong the time spent in eating so that it seems as if he has eaten a lot (but actually hasn't)
For example,when I don't want to eat a lot,I usually choose giant prawns from the menu so that I spend more time in arriving to the 'juicy part'
'engaging other senses...' Well,he's listening to Mozart.He uses the sense of hearing everyday but perhaps listening to Mozart awakes other 'feelings'.The five senses are sight,touch,smell,taste and sound(hearing)-so I'd say at the very moment he's using one less-taste
I would explain it more as having more awareness at the moment.
Hope to see tdol's view on this as well.
Have I been of any help???
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