Not by your standards, apparently.
But by technical and generally agreed upon standards, you'd be wrong.
Weapons of Mass Destruction (WMD) are defined as CBN -- chemical, biological and nuclear. A "dirty bomb" is undeniably "nuclear".
No it isn’t.
A dirty bomb is merely a conventional bomb used to disperse radioactive debris. Lots of things are radioactive. Some soil is radioactive. Gather up a bunch of radioactive garbage and pack it around a large conventional bomb and you have a dirty bomb. It works better if the radioactive debris is dangerous enough to cause panic.
A nuclear bomb is an energy release derived from a nuclear reaction. Energy is created out of matter. There may or may not be deadly radioactive debris produced as a byproduct.