The statements as you present them are both right.
"All students of the University are over 16 years of age. Baby1nut is a student at the university. Therefore Baby1nut is more than 16 years of age." - this is a valid syllogism.
Creighton's statement that "He must be over 16 years of age, for he attends the university is an incomplete syllogism . The conclusion as will be readily seen, stands first." is indeed an enthymeme, i.e. an abridged syllogism (the major premise "All students of the University are over 16 years of age" being left tacit).
The underlying argument of the enthymeme is one and the same with your full syllogism.
There is no problem.
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