Interesting indeed, but I couldn't see one key piece of information on that LTSA page:
What is the definition of a 'fat tyre electric scooter'?
Given this page makes out that these scooters are sometimes marketed as mobility scooters, I'm assuming that they're not talking about ones like Zero scooters? But without a clear definition (and relying on inferred knowledge of what this means) it's pretty damn ambiguous.
It would really p!ss me off if Police start cracking down on e-scooters (being ridden sensibly, he adds quickly) in the current climate of confused regulation and a quickly shifting market; I ride my scooter sensibly, generally wear a hi-vis jacket, always wear a helmet... hell, I even now have indicators I use! And yet every morning I see drivers of vehicles making dodgy calls - often resulting in placing MY life at risk! (What is it about NZers and roundabouts?)