Is GLS an RNAV approach? Short answer is no. It is also not in the framework of PBN.
Out of confusion the naming was not standardized, which led to more confusion. This will be fixed, from 1 Dec 2022 only the term RNP will be permitted for the minima you mentioned. (ICAO Circular 336, starts at page 19)
It stands for area navigation, which is the ability to fly any course in an area, not bound by VOR radials for example.
GLS uses a ground augmented signal, anchor point, course, and slope, so it does just the one thing (like an ILS).
PA, APV, and NPA
Another reclassification will start to impact the older terms precision approach, approach with vertical guidance, and non-precision approach. There will be only two main types, A and B. Here's a Eurocontrol slide that breaks them down, and also shows that GLS is not in the PBN scope:
Last but not least in case any of the above is confusing, this big Airbus presentation (icao.int, Sep 2017) covers the history from conventional navigation to PBN and beyond, and also talks about the GLS.
Addendum based on comments:
- A 'conventional procedure' in the slide above includes NDB, LOC, LDA, VOR, ILS, with or without DME, and MLS approaches. ILS and MLS would fall under PA / Type B.
- For how the GLS plots the approach, see: How do GLS avionics plot an entire accurate approach path?
- One of the things that sets the GLS apart from RNAV is the need for a ground component at the airport, the VHF Data Broadcast (VDB) transmitter.