I guess my confusion was with defining the phrase "spawn a franchise" as "creating a media franchise". Where one could say the first Sonic game on the Genesis lead to the creation of a media franchise that consisted a series of games, multiple animated series, comic books, board games, a film, and so on.

I tend to see the term "game series" used more when just talking about the games, while "franchise" is a much broader term. It was not the Duck Tales game that was responsible for "spawning" it's franchise so that game alone in the list was throwing a wrench into my thought process.