The story
From night + core (“key part of a thing”) via Nightcore, the name of the Norwegian duo that created the genre. They explained their name by saying "we are the core of the night, so you'll dance all night long." Around 2008, others started making their own songs in the same style and used the term nightcore not to refer music made by the duo, but to the new genre of music as a whole. As this usage spread and knowledge of the original duo faded, the term was reanalyzed as night + -core in the same style as other music genres like metalcore, rapcore, etc.
Etymology from Wiktionary, CC BY-SA 4.0.