New Zealand's emissions are a drop in the global bucket - they account for maybe 0.1% of worldwide greenhouse gases - so the direct climate impact from their country alone isn't what you need to worry about. What matters more is what it signals. Their situation is a microcosm of a warming world: glaciers melting there are an early warning sign that the planet's temperature is rising everywhere, and that affects sea levels, weather patterns, and agricultural zones that matter to you regardless of where you live.
The real pitfall people miss is thinking of this as New Zealand's problem to fix alone. These emissions aren't just coming from heavy industry or power plants - a significant chunk comes from agriculture, particularly dairy and sheep farming, which is core to their economy. That creates a genuine tension between environmental goals and livelihoods that most countries face too. They've been working on emissions targets and investing in renewable energy, but progress is slow because the economic incentives point the other way.
So yes, you should care, but not because New Zealand's glaciers melting will directly flood your city next year. Care because it's part of a global warming trend that compounds everywhere - droughts in one place, floods in another, crop failures affecting food prices. The real concern is whether countries can actually make the structural changes needed when those changes cost jobs and wealth in the short term. New Zealand's struggle with that is basically everyone's struggle.