As you said, the extent of character development does rely on the genre. In terms of the content, games will most often pull from the the traditional spatial genres: fantasy, adventure, science fiction, horror, and war that do exactly what Jenkins explains. But in terms of game genre, character development in shooters, for instance, is particularly more difficult to pull off than in RPGs.

Even if most games have terrible character development, that automatically means that some games will have just the opposite. All of the (3D) Prince of Persia games come to mind. And with the most recent one, I felt that what the Prince does at the end, as an example, was perfectly motivated by the development of his relationship with Elika that continuously builds throughout the game.

That being said, only some games need character development to have good narratives. I think the question shouldn’t be “why don’t games contain character development?” but instead “do games need character development in the first place?”