That map of NZ might well be based upon the openstreetmap project. I remember someone must have worked hard, there, to add all those airstrips - an impressive number indeed. My own list of European airfields, consolidated from several public sources and regularly updated, counts a total of 994 aerodromes in the UK, but that includes 213 closed fields.
The figures given by @BossEyed above look quite credible to me.