For a full answer we would need to have further pictures of the back of the insect. However, NZ has few insects of that size range that are at all common, so I suspect that what you have here is a Huhu beetle (Prionoplus reticularis).
The Huhu beetle is a widespread, large, brown beetle that is often in the 40-50 mm (~2 inch) range, with a pattern of reticulated veins on the elytra. They have brown hairs on the head and thorax and long antennae, that are often 1/3 or up to as long as the body. The species are largely known as a "wild food", with the grubs (larvae) eaten raw or fried. They are also fairly heavy fliers and make quite a racket flapping around. Completely harmless to people.
Edited to add: Having watched the video; a couple of seconds from the end you can see the elytra with the patterns on, so I am confident that this is a Huhu beetle.
The larvae are commonly found in rotting wood, particularly conifers (pine, macrocarpa), so if you have those around, that's where they will be coming from.