House Elves have not officially been described as beings in canon, and there is no reason to assume that they are considered beings, given the treatment they receive from wizards. Wratched (talk) 10:40, August 15, 2015 (UTC)
May I point to the Fountain of Magical Brethren? While it is not officially described as such, I got the impression it was meant to portray the "main" Beings under the regulation of the Minsitry of Magic. It certainly does seem to put Goblins and Elves on an equal footing. Scrooge MacDuck (talk) 16:22, June 1, 2017 (UTC)
This would not fit on this page, but couldn't we create a page that lists sapient being and defines sapience? Merpeople, Acromantulas or Runespoor show that several sentient creatures are not classified as Beings at all, but it'd be interested to have all of the "Magical Brethren" in one place.