Which is because they're not hashmaps, they're associative arrays. Article treats them as the same thing, but they're not - that's why the "declare -A" is A and not H - it stands for "associative".
Author of the article here. As far as I care, if it quacks like a hashmap, it's better to describe it as a hashmap. The fact that it's an associative array under the hood is irrelevant.
It doesn't; it's just that you probably never heard the quack of a hashmap so you don't know the difference.
A hashmap is a very specific structure that uses a hashing algorithm to normalize the key sizes, and then usually constructs a tree-like structure for fast key lookups. Anything that doesn't use such an implementation under the hood should not be called a hashmap, whether you care or not.
You have this the wrong way around. Associative array is the abstraction you are talking about. Hash maps are a specific implementation of that abstraction. You could also define hash map as an abstraction which has the same interface as associative array but with more strict performance characteristics. But either way it's wrong because bash is neither implemented as a hash map nor has the performance characteristics of a hash map.
For reference the main implementations of associative array are alists/plists (linear time), balanced binary trees, b-trees (logarithmic time) and hash maps (amortised constant time).