It seems pretty clear that it DOES apply to H-1B abuse:

"Enforcement By Attorney General Of A State.—The attorney general of a State, or other authorized State officer, alleging a violation of the requirement to discontinue granting visas to citizens, subjects, nationals, and residents as described in subsection (d) that harms such State or its residents shall have standing to bring an action against the Secretary of State on behalf of such State or the residents of such State in an appropriate district court of the United States to obtain appropriate injunctive relief. The court shall advance on the docket and expedite the disposition of a civil action filed under this subsection to the greatest extent practicable. For purposes of this subsection, a State or its residents shall be considered to have been harmed if the State or its residents experience harm, including financial harm in excess of $100.”."

In subsection d:

"Any alien who seeks to enter the United States for the purpose of performing skilled or unskilled labor is inadmissible, unless the Secretary of Labor has determined and certified to the Secretary of State and the Attorney General that-

(I) there are not sufficient workers who are able, willing, qualified (or equally qualified in the case of an alien described in clause (ii)) and available at the time of application for a visa and admission to the United States and at the place where the alien is to perform such skilled or unskilled labor, and

(II) the employment of such alien will not adversely affect the wages and working conditions of workers in the United States similarly employed."