Not all regular expression engines work in the way being described here. The step-through in this post demonstrates the (unoptimized) algorithm that Java, Ruby, Perl, Python, and PHP use, which is the recursive backtracking algorithm.
The author should emphasise that point more. The whole point the article makes is moot if regex is compiled to a DFA before use. A DFA will match a character in strictly O(1), so no matter how complex the regex is, strings will always be matched in linear time. Even more, a more “general” regex will typically have fewer states in the DFA than the specific one, so it may be better to use it instead.
All the regexes she used in the article are in fact “simple enough” that the Thompson algorithm and subset construction work, so maybe an example that actually uses the fancy features would be more illustrative.