A wallet consists of a rectangular cardboard package that is similar to a digisleeve (gatefold on MB) except that the disc or discs slide horizontally into a vertical slot inside the packaging.

https://en.wikipedia.org/wiki/Optical_disc_packaging#Wallet

Currently, digifiles seem to be the closest (they have the slot vertically as opposed to being horizontal), but adding a separate type might be a better approach. These are not gatefolds because the slots are on the inside of the packaging.