As you can see, rather than being enforced by the EEOC or a state agency, it is enforced by the Office of Special Counsel for Immigration-Related Unfair Employment Practices of the Department of Justice. From the FAQ Page for OSC, here's what the Act prohibits, which also includes national origin discrimination for employers not covered by Title VII and retaliation against those who participate in the OSC process:
*Citizenship or immigration status discrimination with respect to hiring, firing, and recruitment or referral for a fee, by employers with four or more employees, subject to certain exceptions. Employers may not treat individuals differently because they are, or are not, U.S. citizens or work authorized individuals. U. S. citizens, recent permanent residents, temporary residents, asylees, and refugees are protected from citizenship status discrimination. Exceptions: permanent residents who do not apply for naturalization within six months of eligibility are not protected from citizenship status discrimination. Citizenship status discrimination which is otherwise required to comply with law, regulation, executive order, or government contract is permissible by law.
* National origin discrimination with respect to hiring, firing, and recruitment or referral for a fee, by employers with more than three and fewer than 15 employees. Employers may not treat individuals differently because of their place of birth, country of origin, ancestry, native language, accent or because they are perceived as looking or sounding "foreign." U.S. citizens and all work authorized individuals are protected from national origin discrimination. The Equal Employment Opportunity Commission has national origin jurisdiction over employers with 15 or more employees.
* Unfair documentary practices related to verifying the employment eligibility of employees. Employers may not, on the basis of citizenship status or national origin, request more or different documents than are required to verify employment eligibility and identity reject reasonably genuine-looking documents or specify certain documents over others. U.S. citizens and all work authorized immigrants are protected from document abuse.
* Retaliation. Individuals who file charges with OSC, who cooperate with an OSC investigation, who contest action that may constitute unfair documentary practices or discrimination based upon citizenship status or national origin, or who otherwise assert their rights under the INA's anti-discrimination provision are protected from retaliation.
My recollection is that the OSC has been around since the mid-1980's without a lot of impact, but when immigration heats up again as it inevitability will, it's good to be aware of its existence.
Particularly for those small employers who don't normally have to worry about discrimination.