The official line of the New Zealand Government is the same as the United States and Australia in that they take no position on competing claims to sovereignty over disputed land features in the East China Sea and South China Sea. Claims of territorial waters and EEZs should be consistent with customary international law of the sea and must therefore, among other things, derive from land features. Claims in the South China Sea that are not derived from natural land features as recognised by UNCLOS are fundamentally flawed. That territorial disputes should be resolved peacefully, without coercion, intimidation, threats, or the use of force. That parties should avoid taking provocative or unilateral actions that disrupt the status quo or jeopardise peace and security. New Zealand wants to engage with China and all other nations that follow international norms and behaviours which recognise international law and dispute mechanisms. New Zealand's strategic hedge is that it is balancing its trading and positive relationship with China whilst maturing its security and commercial relationship with the United States as a counterpoint.
China’s EEZ as recognised under the United Nations Convention on the Law of the Sea (UNCLOS) is relatively small at 879,666 km2 (where as Japan’s is 4,479,388 km2). This is a starting point to explain its assertive claims to many disputed islands in the region - China feels landlocked and it wants to control its sea-lane approaches and an expanded EEZ gives it that but also increases its rights of exploitation over all natural resources (fish, etc.), nonliving resources (oil, gas, minerals, etc.) as well as potential development rights of energy sources. It is undertaking a salami slice approach in incrementally pursuing its claims and creating islands, because does not want to get push back though it probably knows pushback will happen eventually.
China is not on evidence a direct threat in a classical military sense to New Zealand nor to Australia. However, its current SCS and ECS behaviour is outside mature rules based international behaviour in that it does not attempt to utilise international legal mechanisms to arbitrate its disputes using an evidence based framework. This means that it has a potential threaten to peace, good order and security in the region, which is a threat economically to New Zealand and its interests.