But what are Germany's laws about discovery? This seems like a problem that would have occurred even before computers: if an executive is handwriting letters at home to engage in illegal activity for the benefit of their company, does a German court have authority to search the home?

This is an American case, and it's being litigated in accordance with American law, so the judge is using American rules about employment to achieve the goal here. I would be surprised if there weren't some way to accomplish the same goal in Germany.