It upsets Sheldon when you play with the food...It upsets Sheldon when you play with the Sheldon. First sentence I kinda can justify the, second one - just don't get it.
(The big bang theory. https://www.youtube.com/watch?v=mCK6ZwpNICQ)
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It's just a jokey continuation of the conversation. Prior to this there are several instances where they say, "It upsets Sheldon when you play with the X."
It also jokingly insinuates that there is only one 'Sheldon' in the world and at the same time dehumanises him somewhat.
'the' is known as the definite article (as opposed to the indefinite 'a' or 'an') and implies that something is special, important, significant or one of a kind. You can't go to an Eiffel Tower, but you can go to the Eiffel tower. Often in speech we misuse this article in order to imply that something is more important than it is. 'the Sheldon' is probably mocking Sheldon's self-important perspective of himself.
It's also a rhetorical technique known as parallelism, to emphasise the place value of the word as an object in the sentence.