There is no such thing as RNAV-1 (GNSS) just that a GNSS can be used as one way to be RNAV-1 approved.
Europe uses P-RNAV, there maybe some ANSP's using RNAV-1 as the standard, the main difference being that RNAV-1 requires the aircraft to follow guidence from 500ft, P-RNAV does not.
Neither standard requires the use of GPS at all, however, many aircraft use their GPS/GNSS as a means of compliance with the relevant standard.
With regard to the OP could he tell us for which airport he is refering, as some ANSP's do levvy a few of their own requirements depending on if the method of RNAV-1 compliance is GNSS based.
Eg. Many of the US airports require RADAR if the method of RNAV-1 compliance is not GNSS - even though the ICAO standard does not.
PT6A