How do you rank the strings represented by a regular expression?
Suppose you want to encode an element of $\binom{[n]}{k}$, that is, a subset of $\{1,\ldots,n\}$ of size $k$. There are $\binom{n}{k}$ such subsets. FPE functions know how to handle encoding and decoding of integers in the range $\{1,\ldots,M\}$, for an $M$ of your choice. To use such an FPE function in your case you will have to translate an element of $\binom{[n]}{k}$ to an integer in $\{1,\ldots,M\}$ for $M = \binom{n}{k}$ (ranking) and back (unranking), efficiently.

How do you efficiently rank and unrank elements of a domain like $\binom{[n]}{k}$? For which domains is it possible? The video describes one scenario where this is possible, and one general algorithm for handling this scenario. If your scenario is different then you might still be able to rank and unrank efficiently, but you will have to use a different approach.

The scenario described by the video (which I haven't watched) is probably that of languages accepted by a DFA with a small number of states. Such a language can be ranked and unranked efficiently, and the algorithms use the DFA which accepts the language. This is how the DFA comes in – it is used by the ranking and unranking algorithms. Hopefully these algorithms are described in the video, but otherwise you can ask another question here.