DSi-Enhanced means that the game features something extra when run on a DSi console instead of a DSPhat/Lite.
DSi-Enhanced features will only work with an original cart only primarily because the DSi has not been cracked.
Anyways, the game currently isn't running on the publicly available AKAIO 1.6 RC2 or the Acekard software OSes. It does run in the private version of AKAIO 1.6 Final (from what i've been told.)
Also when any DSi-Enhanced game runs on a DS/i flashcart, it will only run in DS-Mode which means the DS/i can not access whatever extra feature the company put in for the DSi-Mode.
There are also a few DSi-Only games but it is unlikely there will be anymore than a few. Mostly because the DSi-only games make heavy use of the cameras and companies want a wide base of sales. Alsowith DSi consoles being a smaller portion of the DS handheld community there are not going to be very many DSi-only games.