Are watercolor paints in a tube considered a liquid by the airlines?
The general rule of thumb is if you can squeeze it, pour it, or spray it, it's a liquid. If I'm thinking of the right thing, watercolor paints qualify and will have to go in your checked luggage (unless under 3 oz. in which case it could go in your quart-sized ziploc).
You asked about the airlines' definition, but it's actually the TSA definition that counts; TSA says liquids and gels but I haven't seen a TSA definition of exactly what's a gel , but am guessing Liz's definition is applicable and TSA will say it's a gel.
If it's considered a gel, then it's subject to the 3-1-1 rules for carry-ons. And if, for that reason, you have to put it in checked baggage, put the paint tubes inside zip-locks or something else that will contain any leakage/oozing of the paint, which can be caused by fluctuations in air pressure in the baggage hold. You don't want clothes decorated by your paint!