PlatformIO doesn’t support a repo that has multiple libraries. It will always look for the first manifest file (library.json,package.json, etc.) or the examples/ folder and then only copy that subpath from it. (See How can I create a repository with multiple libraries in it on GitHub and use them in a project? - #3 by pfeerick).
As the readme says, even installing this library in the Arduino IDE requires adding symbolic links from the sub-folders to the main libraries folder, which is completely abnormal for a regular Arduino library.
In PlatformIO, you should download the library once and copy all sub folders in the lib/ folder of your project, so that lib/PN532, lib/PN532_HSU etc exist.