Unfortunately, that law has some huge loopholes. The same criminal who could not buy from a store can easily go online and purchase whatever kind of weapon he/she wants, or they could go to a gun show and do the same. But when Congress tried to close those loopholes, the NRA (and other nuts) screamed that the proposal violated the Constitution and the government was coming to confiscate everyone's guns. It was a ludicrous lie, but it convinced enough politicians who wanted NRA money to vote against the law (and to protect the non-existent right of criminals to buy guns).
Why does the NRA's leadership want to keep it easy for criminals to buy guns? Are they just stupid, or are they being paid off by gun manufacturers (that don't care who buys their product as long as they can sell more guns)?