Yes, it is. It was built on the request of Princess Christina, youngest sister of princess Beatrix, by architect J.B. baron van Asbeck in the 1980s.
Christina and her family lived there until the divorce of Christina and Jorge.
Villa Eikenhorst is located at (private) the royal estate De Horsten which has been in the royal family for a long time - it was first bought by Prince Frederik, second son of King Willem I. In 1903 queen Wilhelmina bought it from her greataunt princess Marie (Frederik's youngest daughter), it was passed on to queen Juliana who passed it on to her eldest daughter princess Beatrix who donated it to her eldest son in 2017. There are a few other houses on the estate, including the ones where the king's cousins prince Pieter-Christiaan and prince Floris live with their families. His cousin princess Margarita and her family also lived at De Horsten for several years.