If you read the article you will read about two reactors that are actually fueled by what we consider waste today.
That we don't completely burn the fuel used in a reactor is a 'bug', a misfeature if you will. That was expedient when the initial reactors were being brought online and now is a regulatory pain in the butt. There is nothing in the physics that requires a nuclear reactor complex to generate nuclear waste of any kind[1]. Only in the regulations.
[1] Nuclear incineration of even low level waste can effectively convert anything that was once radioactive into short lived nucleotide. Converting everything burned into its lowest energy stable state. But we don't do that either.