I'm glad that you like my solution, but please note that, as another commenter said, it's a buggier version of the original regex I thought of ("^(dict|here)+$"), which I think should work but doesn't, at least not in Python.
I suspect it's because the match group is being replaced with the last match rather than added as another group, but it will work as a state machine, and is pretty much equivalent to the backtracking example in the article (although with much less code, and no memoization).
That said, I think that the reason interviewers ask about functions for which we have well-known implementations is to see whether or not you know how they work and/or could implement them yourself. Nobody will reasonably expect you to implement your own string comparison routine, but you could score points if, for example, you said Boyer-Moore for string searching rather than the naive iterative version.