It does, but the article actually doesn't define n and it's confusing.
In the common case, where s is short and the dictionary is big, the size of the dictionary probably matters most to the running time. s is likely a cache line and a handful of instructions to compare — whereas the dictionary probably doesn't fit in L1 or L2, maybe not L3. Obsessing about algorithmic analysis based on the string size instead of the size of the dictionary gives good signal for whether the candidate is a pedant, and poor signal about engineering.
In the common case, where s is short and the dictionary is big, the size of the dictionary probably matters most to the running time. s is likely a cache line and a handful of instructions to compare — whereas the dictionary probably doesn't fit in L1 or L2, maybe not L3. Obsessing about algorithmic analysis based on the string size instead of the size of the dictionary gives good signal for whether the candidate is a pedant, and poor signal about engineering.