You didn't say it was the "only" one, but you did stipulate it as
a qualifier, so to belong to the 'dragon' category, it has to meet all your qualifiers, which the green and blue dragonflight don't. And if all the qualifiers aren't met, then they don't belong to that category.
For example: "bikes are motorized vehicles that use fuel to run, and can carry a passenger, and has two wheels" , meaning that, to be considered a bike, it has to have an engine, it has to use fuel, has to be able to carry a passenger, and has to have two wheels. But if not all qualifiers need to be met, then trucks are bikes, motorized lawnmowers are bikes, houses are bikes, etc.