All that law is saying is that that specific law does not grant the President authority to regulate, it does not supersede any laws that do grant Presidential authority to regulate imports.

Tarrif authority granted to the President was done by the 1934 Trade agreement act, 1963 trade expansion act, and the 1974 Trade act. They give the President authority to impose tarrifs, for nantional security, nantional emergencies, or unfair trade practices. Even in those cases Congress has the ability to limit the president's power to impose tarrifs as they have the ultimate authority outlined in Article 1 section 8 of the constitution.