I don't agree with this author's opinion as stated. The written word doesn't have or need an intonation. Intonation matters if we translate this written passage to speech, but text does not need to be translated to speech in order to be comprehensible.
The joke only succeeds if the reader assigns appropriate semantics to the punchline. Similar semantics can be carried by an entirely different set of words:
A grasshopper walks into a bar and gets the bartender's attention. The bartender asks "Hey, did you know that we have a drink named after you?" The grasshopper replies "That's interesting. I'd like to try it. Give me a Norman."
Performing surgery on humor is a risky undertaking. It often leaves the patient severely weakened if not dead. In this case, I think the humor has survived, even if the punchline carries a little less punch. However, this version of the punchline employs a command (well, a request) rather than a question, which would be spoken with an entirely different intonation.
In the original version, the joke fails if the reader mistakes "Norman" for the bartender's name. My version doesn't afford the same mistake. We could also eliminate that inappropriate ambiguity by paraphrasing the original as a more complete question: "You have a drink named Norman?"
This distinction between "Norman" as a form of address and "Norman" as the heart of the question can be represented by a difference in intonation. This author seems to mistake representation for identity. Intonation is not strictly necessary to mark this distinction and it is certainly not the same thing as the distinction so marked, even though it is commonly used and commonly understood, and happens to be quite effective.
Any version of this joke is likely to fail if the reader doesn't recognize "grasshopper" as the name of both a cocktail and a suborder of insect. The bartender intends that "named after you" be interpreted as named after your kind, but the grasshopper infers that it means named after you as an individual. The humor relies on subverting one obvious expectation with another, and the subversion is destined to fail if the first intended expectation is not obvious to the joke's audience.