As the article states the initial pay gap was because of his Dr Who work, meaning that he was a bigger draw to the show. The issue is why he continued to be paid more in the second season where he had a much smaller role and after she was recognized for her role in the show with a number of awards.
He was the far bigger star when the first series was cast and Netflix publicised it off the back of his Dr Who fame, so it's understandable he got more at the outset. But that's no excuse for them to continue paying Claire less for series two, when it was her performance that made The Crown the success it was. Someone at Netflix should be writing her a big fat cheque this morning to make up the difference!