The headline is misleading. All this rule change does is do exactly what you said above, make sure the law applies the same to everyone who is legally in the U.S. except for diplomats and criminals. When it comes to buying guns from federally licensed dealers, the same rules now apply to legal aliens and to U.S. citizens, when it comes to buying guns from federally licensed dealers. Before this change, legal aliens were held to a different standard.
the extra “when it comes to buying guns from U.S. dealers” is an editing error and redundant.