How do you know that work was the primary reason for the arrests? There is overwhelming evidence that the desire to exterminate certain groups of people was not to build a canal or something, but to kill them while preserving a facade of functioning jurisprudence. Work was just an added benefit, just like the gold tooth fillings that the Nazis got from the corpses.
Williamson is not denying the mass murder. He questions the method of the murder, which has become a symbol for some people. But questioning the historicity of the symbol is not questioning the underlying truths.
Contrast that with sending arrested victims straight away to special treatment in a system designed to handle 2,500 such victims per hour (Auschwitz-Birkenau), a victim which Williamson denies existed.
Choose your terms carefully. He does deny the mass murder of more than 5.5 million Jews, and he at least implies that the 200,000-300,000 dead Jews he will admit died merely did so incidentally.
He's taking his cues from Fred Leuchter, for goodness sake. Don't try to pretend he is not denying the Holocaust.