What does "potted" mean in "Potted Potter"?
It means shortened or compressed. For example, potted history is a frequently used phrase that means a history that is abridged.
As the website you link to says:
All seven Harry Potter books in seventy hilarious minutes!
So [Harry] Potter has been potted.
Potted in this sense is recorded as chiefly British usage.
Abridged.
Literally, a method of cooking or preserving (in a pot), but often used to refer to a condensed form of e.g. a book.