Based on the photos, They appear to be third party as I haven't seen a white, corded, Gamecube remote, and Nintendo never made two-tone Gamecube remotes.
First party is from Nintendo, second party means the manufacturer is partly owned by Nintendo, and 3rd party is from companies that aren't affiliated with Nintendo. For example: The Nyko Wands are 3rd party because they aren't made by Nintendo and Nintendo doesn't own Nyko.