To my understanding, Casinos in the USA can only be owned and operated by Indians on their reservation.
This is not accurate.
Las Vegas, Reno, Atlantic City, Detroit all have non-Native American casinos and there are many others dotted around the US.
Most states do outlaw gambling but this has become much more relaxed in the last 20-30 years.
As for California, it permits some form of gaming, usually cardrooms which are distinct from casinos.
Licensed cardrooms may offer approved card games in which players vie against each other (rather than against the house), such as poker. As of 2011, there were 93 licensed cardrooms in the state. Since 1998, there has a moratorium on new cardrooms.
Non-banked card games such as poker have always been legal in the state. The California Penal Code, enacted in 1872, prohibited several casino games by name, as well as all house-banked games, but did not outlaw poker. Statewide cardroom regulations were enacted in 1984
As for Native American casinos, these are more prevalent as
federally recognized tribes can operate casinos under the federal Indian Gaming Regulatory Act and tribal-state compacts negotiated with the state. As of 2006, 55 tribal casinos were operating in California
Nevertheless, enforcement would be down to local officials, generally, and in the show the town is incredibly corrupt. Even if the casino was operating illegally, it's likely that someone was paid off to look the other way.