Illusory Dragon specifically is not a creature
It's referred to repeatedly as an illusion rather than a creature (XGtE, pgs. 157-158):
By gathering threads of shadow material from the Shadowfell, you create a Huge shadowy dragon in an unoccupied space that you can see within range. The illusion lasts for the spell's duration and occupies its space, as if it were a creature.
When the illusion appears, any of your enemies that it can see must succeed on a Wisdom saving throw or become frightened of it for 1 minute. If a frightened creature ends its turn in a location where it doesn't have line of sight of the illusion, it can repeat the saving throw, ending the effect on itself on a success.
As a bonus action on your turn, you can move the illusion up to 60 feet.
Compare this to Phantom Steed, as you mention in your question (PHB, pg. 265):
A Large quasi-real horse-like creature appears. You decide its appearance, but it is equipped with a saddle, bit, and bridle. Any of the equipment created vanishes it is carried more than 10 feet away from the steed.
For the duration, you or a creature you choose can ride the steed. The creature uses the statistics for a riding horse, except it has a speed of 100 feet.
However, the Illusory Dragon can be targetted by attacks, although they automatically miss/always succeeds saving throws and is immune to damage.
The illusion is tangible because of the shadow stuff used to create it, but attacks miss it automatically. it succeeds on all saving throws, and it is immune to all damage and conditions.
For this to make any sense, it must follow that it can be targetted by attacks and spells, even though it isn't a creature.