yes, it does cost money, and typically is rather expensive (~$5k USD) to file a patent application because it usually requires a lawyer's help, and IP lawyers are expensive. There are special circumstances under which the cost to file can be waived - https://info.legalzoom.com/file-us-patent-20189.html - but seeing as how NXIVM was backed by Bronfman sisters financially, they'd have no reason to request patent fees be waived (although this patent seems to be assigned to the company First Principles Inc. [though the inventor is listed as Keith Raniere] - I have no idea what that company is, or if it's a subsidiary of NXIVM). Definitely an odd patent though - seems like something happened with it as early as 2007, but the application for it wasn't actually filed until 2013. Not really sure what else to make of this.