Does the moon have any affect on earthquakes being created?
The forces involved in the New Zealand earthquake are not amenable to precise evaluation - at least not without detailed geotechnical evaluation, but we can use the peak ground acceleration as a proxy. For a magnitude 7.5 earthquake the peak ground acceleration is about 0.4g. Compare this to the normal moon's gravitational acceleration on Earth's surface of about 3.318 E-5 g. 'Super-moons' are about 16000 km closer than usual, yielding a gravitational acceleration of 3.783 E-5 g. Therefore the differential gravitational acceleration of a super-moon, compared to a normal moon, is about 4.65 E-6 g. Or to put it another way, the effect of a super-moon is to create about a 0.001% of the acceleration (and hence force) required for the accumulated strain energy to overcome friction, and hence cause the earthquake. This assumes that all of the moon's gravity was aligned in such a way as to exacerbate strain along the slip plane - which is never going to be the case. 

I suppose that one could argue that the miniscule gravitational force of a super-moon could have been the 'straw that broke the camel's back', but the accumulated strain energy in the ground must have been so great that the earthquake was about to happen anyway, with or without the moon's gravity. 

Afterthought: With the boot on the other foot: The Earth's much larger gravitation has an effect on the Moon. There are moon tides which cause regular, small but measurable moon-quakes. See Moritz and Melchior (2013), Tidal Interactions in the Earth-Moon System.