The key statement there is 'on account of his nationality'. Wynn's SA nationality does not allow him to represent NZ. That's why section 6 is not applicable, and why section 7 is (and hence why he's not eligible without an exemption).
Article 6 most likely doesn't apply but not for the reasons you suggest.
NZF may have been wrong all along in thinking that Wynne qualified under Article 6 because he has two nationalities.
Actually, Wynne most likely no longer has South African nationality because according to media reports he became a New Zealand citizen and has held a NZ passport since January 2015. Tragically, this would have almost guaranteed the chance of success of an appeal to FIFA under Article 8 to change the Association for which he plays, because he is in fact probably no longer eligible to play for South Africa.
This will probably help Storm Roux's case too if he wants to apply under Article 8.
When a South African adopts another nationality when they are aged 18 or older, they automatically lose their South African nationality - unless they apply to retain it beforehand:
http://www.sahc.org.au/citizenship/Dual_Citizenship.htm
"The South African Citizenship Act provides for retention of South African citizenship PRIOR to the acquisition of a foreign citizenship. A condition of attaining dual citizenship for all South African citizens aged 18 years or older is that they must apply and be granted permission to retain their South African citizenship prior to the acquisition of a foreign citizenship.
If a South African citizen does not obtain this prior permission they will automatically lose their South African citizenship on voluntary acquisition of a foreign citizenship."