Dsi games come in two varities: DS games that feature special features when used on the Dsi (i.e. Camera in Pokemon Black and White). Then there are Dsiware games, those which you buy from the Nintendo Shop with Wii/Ds Points.
Currently, no one has hacked the dsiware games to make backups playable on a ds, dsL, dsi, or dsi XL. Furthermore, backup DS games that have the extra DSi features do not function during game play (The regular game works, it's just the extra feature that don't work). (At least that's my understanding of it)