Looking at the notice it seems these people bought plots long ago...and then it says: NO BURIALS HAVE BEEN PERFORMED IN ANY OF THESE SECTIONS.
So that implies they are not buried there at all, just never used their plots. Rombout Cemetery is a non-profit historic Cemetery with an appealing history-focused web presence complete with footnoted references.
The website also has info about the option of buying a new plot in the open section of the cemetery, including pricing, so this seem to be a very up-front sort of operation.
The notice identifies John Waldo the purchaser as born June 2 1846 and that matches the wikitree profile for my second cousin three times removed. John Bruce Waldo was buried elsewhere with his parents:
John Bruce Waldo was the great grandfather of Actress Lee Remick. She had two children, one of whom is mentioned in the notice: Matthew R. (Remick) Colleran, and a daughter Katherine Lee Colleran, who has two children born in the 1990s. Likely John Waldo has many living descendants.
Probably these heirs could have some legal claim to the plot, but if unclaimed it will be donated and not sold, so overall this seems reasonable with respect to respecting John Waldo. Not sure about any of the others who are listed.