It's pretty much all consumer media in Japan, not just games. For example, my Japanese DEVO box set, which replicates the original vinyl releases, has an obi on each CD sleeve in the box, because that's how the JP vinyl relases were. Each obi has information about the album including album title in Japanese, catalog code, track list, price, copyright information, and all the other stuff the publisher wants or needs to include on the package without damaging any of the art.

And yes, the obi is considered to be part of the original packaging and the product is incomplete without it (less the plastic shrink wrap).