Actually brickwork in the traditional sense is very rare in NZ, and would not have been allowed in new construction for many years. What is quite common is what is called brick veneer, where the frame of the house is wooden, but has a single layer of bricks attached to the framework with metal straps nailed to the frame and trapped in the mortar between the layers of bricks. This has been shown to perform quite well in earthquakes, and in the worst case the bricks will end up on the ground around the house. While this is not good, if the earthquake is that severe you don't want to be close to any sort of building. In the North Island, where I live, it has always been noticeable that there were more brick veneer houses as you travelled north through the Waikato and on to Auckland. This was mostly because the earthquake risk is lower there.
Christchurch in particular had a problem with a lot of older buildings that were built with brick in the more traditional way, especially older shops. These tend to be particularly bad since they have large openings at the front for the doors and windows, often with a heavy facade above. But then, the largest number of casualties were in a relatively modern building where both the design and the checking of it were incompetent.
One thing you can see in the pictures is the complete failure of a chimney at the Waiau pub. That is an old building, and it looks like the chimney will have been done with the old style lime mortar. This was not all that strong even when new, and deteriorates with age. Those bricks will have been sitting on a weak layer of lightly bonded sand and as you will see if you go looking for pictures of the quake on the web, the brickwork has just turned into individual bricks.
There will be some high rise buildings in Wellington demolished as a result of this quake. It should be noted that designing for earthquakes means that the building should not collapse during the quake, it does not mean that it will necessarily be usable afterwards. In absorbing the energy, the reinforced concrete is likely to turn into a steel cage full of rubble. Although Wellington is quite a way from the epicentre, this quake went on for quite a long time, and apparently this was quite hard on the buildings.
John