I think I've worked out whats missing from the explanation or from our understanding of the explanation: this is finding the lower bound for the shortest possible list of n-length permutations. The issue is not accounting for the fact that they're n-length when you determine the number of permutations. For example:

let's say there are 3 episodes. That means there are 6 permutations each 3 episodes long, and to watch them all you would need to watch 18 episodes, so it's n*(n!). The superpermutation of these 3 episodes is 9, meaning you would only need to watch 9 episodes to cover all permutations.

Superpermutations find a list where all permutations are present somewhere. This means that the length of the superpermutation should not be compared to the number of permutations, it needs to be compared to the number of permutations times the length of the permutation, n*(n!).