I would think in a pragmatic sense that after the war in Germany it would have been awfully hard to find anyone who was an adult who was not a Nazi Party member to work the government. No, party membership was not compulsory, but it certainly would have kept them out of your business if you were. Sort of like the Communist Party in Russia was not compulsory, but strongly recommended.
I don’t find this story remarkable unless they had a high party official with blood on his hands and uniform working there, and the article does not say that.
Actually, Adenauer sought non-Nazis for his government. They did exist, as he was one himself. There were others too, but the NAZI party was also a jobs program, so the people with the expertise in running the quotidian aspects of government were often NAZIs. There were many, however, who would have done just as well. He found them in the NAZI prisons,for example, Stadelheim. Some effort would have found them (and sometimes did).