Rayquaza is the Sky High Pokemon, not the Dragon Pokemon. :P
Maybe this further helps:
The Japanese name of this move literally means "to paint a dragon and dot its eyes" and serves as a metaphor for the finishing touch in a piece of work that gives it "the spark of life". The idiom originated from a legend where Zhang Sengyou, a Chinese painter, completes the dragons on a mural by dotting their eyes and thus literally bringing them to life; they spring out of the temple wall and fly off. The completed dragons immediately ascended to the heavens after the work was done.
In the legend it was based off of, the dragons (similar to Rayquaza in this instance) ascend to the heavens after the work is done.
So, essentially, Rayquaza represents the sky (Groudon the land, Kyogre the sea), and a legend depicts dragons ascending, (not to mention its abilities are Air Lock and Deltra Stream, relating to air and protecting Flying Types respectively) so it is a Flying Type Move.
Hope I helped!