I agree. Additionally, the words "distinct" or "cardinality" don't appear anywhere in this article, which is a major omission when discussing HyperLogLog. The primary use of the algorithm is to provide a cardinality estimate.
They may not specifically use the word "distinct" (opting for phrases like "unique visitor" instead), but they certainly make the concept clear.
And the problem posed was not to count the number of visitors, but to count the number of different people who visited... the fancy word for that is the "cardinality of unique visitors" but "number of different people" is just as accurate.
Counting the number of people could NOT be done with the same amount of space. This example required two simple counters on the blackboard... call it 30 bits of memory, assuming you didn't expect either counter to get more than 8. That's just about exactly enough space to store ONE social security number... and nowhere near enough to count the unique people.