One explanation I've heard is that this isn't even necessarily about Jones and Infowars violating those sites' Terms of Service, but about those sites insulating themselves from lawsuits.
Jones and Infowars are facing a number of lawsuits, particularly from Sandy Hook parents who have been repeatedly doxxed and harassed and sent death threats by Infowars viewers. (One family has had to move seven times and has not been able to return to visit their son's grave.) What Facebook, YouTube, et al are likely worried about is that if the suits against Infowars are successful, they'll be next, because they gave Infowars a platform.
It would be very hard for the plaintiffs to win that case, especially since those companies have armies of lawyers, but they don't want the bad press associated with it and so have kicked Infowars out in order to try to forestall any such suit and get themselves some good press.