This gets muddy–so at “core”, legally, the States do not have criminal law jurisdiction over tribes. However an act from the 1950s called Public Law 280, specifies a few specific States where the State will have criminal law jurisdiction over tribes in that State, it also allows for additional States to join this framework with the consent of local tribes, a number of States have gotten that consent (the tribes that consent to this are generally doing so in exchange for receiving various State government services which the tribe would be hard pressed to provide.)
States not covered by Public Law 280, essentially were nearly powerless to stop Indian gaming at all. States covered by 280, could stop Indian gaming solely on criminal law grounds, and only if it treated Indian gaming the same as any other type of gaming. This came to a head in the 1980s when California asserted it was going to stop an Indian casino under 280. The Federal courts ruled against California, basically saying 280 gave California criminal law jurisdiction in tribal lands, but nothing else. California operated a State lottery, a form of gambling. In the court’s opinion, this meant that the Indian casino wasn’t violating a California criminal law against gambling, but simply violating a California regulation on gaming, and 280 did not vest California with any regulatory power.
This would have led to probably an explosion in Indian casinos popping up in States not covered by 280, which might have been very unpopular in a number of States. At this point the Federal government stepped in and passed the Indian Gaming Regulatory Act in 1988. Unlike States, the Federal government has generally broad authority over the tribes (the States have very limited authority, for example their authority under 280 requires some level of tribal consent, and is actually a delegation of Federal power to the States, not an innate exercise of State power.)
Under the IGRA, gaming is broken into three Classes. Class I is basically “traditional Indian gaming”, these are “small games of chance for low stakes”, the States cannot regulate these at all, and these are allowed basically in any tribe anywhere without any State interference.
Class II are basically bingo halls and poker halls (technically, any card game where there is no banked cards and the card players are exclusively playing against other players, and not the house), Class II gambling tribes are allowed to operate basically without State interference if that State allows any similar sort of gaming of any form. If the State does not allow Class II gaming generally, the State can grant permission for a tribe to operate a Class II establishment, but is not required to do so.
Class III are essentially full casinos, with slot machines, dealer card games etc. Class III gaming has to be approved by the Indian Gaming Commission, which requires a compact to be negotiated between the State and the tribe, said compact has to also be signed off on by the Department of the Interior.
Since the North Carolina casinos are Class III facilities, North Carolina had to give its consent in the form of a tribal-state compact.