The Pali Kai Cottage rental in that ad is part of cluster of private residences/vacation homes on the Kauai Lagoons cliff overlooking the Marriott complex below.
A little history: Those homes were built by developer Chris Hemmeter in the 1980's as part of his huge visionary plan for Kauai Lagoons and the opulent Westin Kauai Hotel. The Westin Kauai struggled financially from the start, and Hurricane Iniki sealed its fate in 1992. Westin never reopened the hotel after the hurricane and it sat in a mothballed state for quite some time. Marriott acquired the property in 1994 and transformed it into the present-day timeshare complex. During its brief zenith from 1987 to 1992, the Westin Kauai and Kauai Lagoons comprised one of the great luxury resorts in the world. I had the pleasure of visiting the Westin Kauai Hotel just two months before Hurricane Iniki hit, and it really was an incredible place (although some justifiably described it as over-the-top). I even bought a coffee-table picture book of the resort. Back then the entire resort was filled with Asian art treasures. There were mahogany boat taxis and gondolas in the lagoons that would transport you to three different shopping and dining complexes with a total of 12 different restaurants. You could also take carriage rides around the golf course drawn by Clydesdale horses. Helicopter tours of the island took off directly from the resort. During that period, I'm sure those adjacent vacation homes on the cliff were considered some of the most desirable in the Hawaiian Islands and must have sold for an incredible price. You wouldn't recognize much of the resort's former glory from what you see today at the Marriott. In addition to the timeshare renovations, Marriott toned-down the resort considerably so that it resembles what we see today at the Kauai Beach Club. Perhaps the biggest transformation was that Marriott removed the large central pond/fountain (complete with galloping horses spouting water) and replaced it with the beautifully-landscaped courtyard that you now see at the bottom of the escalator. Believe it or not, that entire area used to be a huge water feature.
From the claim in the rental ad, I can only assume that the original deed for those private residences on the cliff likely also included some sort of guaranteed access to the facilities of the hotel and/or Kauai Lagoons. As the developer, Chris Hemmeter was certainly in a position to make that arrangement. When Marriott acquired the property after Hurricane Iniki, they likely inherited that obligation as part of the package deal.