I don't think there's anything like this in the United States. In Europe, I have no idea. There's private investigators, but nothing of the sort of forming a months-long flirtation/affair in preparation of divorce.
But there article is very fair...there are LOTS of strange and novel Japanese phenomenon that fascinates people in other countries. Even in this article, they describe hiring actors to appear as family members at events. That certainly doesn't exist in the United States.