ICAO DOC 8168 p 520 specifies RNAV RNP DEP criterion
Not quite. It specifies that the Basic RNP-1 navigation specification (as defined in the PBN Manual) can be used to develop RNAV(GNSS) departure procedures. That navigation specification (plus RNAV 1 & RNAV 2) does not require RF functionality. If RF turns are included, then that has to be addressed in national standards.
I believe both Australia & NZ have developed their own RNP(AR) departure crtieria...