What's far-right?
Extremist right-wing, Fascist, Ultra-nationalist, white-supremacist, Neo-Nazi, etc. The terrorist had a Neo-Nazi symbol and references on his weapons.
Like all extremists, their deranged warped brainwashed view of the world is one of an Armageddon war between their kind and the rest. A belief in the primitive doctrine of 'might is right' and some devine or otherwise supremacy of their kind to justify their systematic criminality, violence, mass-murder and even genocide against those they hate and dehumanise. Usually they idealise medieval social order and ancient beliefs/myths and so despise modern society and its democratic institutions which they want to bring down by force.
Strip that all down and they are just sicko oxygen thieves who blame and hate others for their own failures, insecurities and inadequacies be that physical (this terrorist was short in stature), intellectual (he failed school) and/or emotional (he showed none - only an evil twisted psychopath would shoot a 2-year old in cold blood). The terrorist also suffered from another insecure loser trait: cultural cringe - as he viewed himself as an European rather than Australian despite being Australian born. He can now rot in some Kiwi jail for the rest of his pointless existence.