No, because if nothing else we don't actually know what it's composed of. It's entirely possible that it will turn out to be a new family of particles, for example.

But more to the point, dark matter is certainly not made up of quarks and/or electrons (because it doesn't interact electromagnetically), so shoehorning it into a list of phases of "normal" matter is misleading at best, if not simply wrong.

A phase/state is usually tied to structure and/or energy of matter. Dark matter is the blanket term we give to particles that interact (observably) through gravitational forces.

In general, cosmology is concerned with the quantification and characteristics of dark matter through observation, so a cosmologist is likely to mean the congregation of dark matter in the universe. Particle physicists are generally concerned with direct observation and characteristics through experiment.

I don't know who messed with the wikipedia article on state of matter, but they're wrong.

I was under the impression that the term "dark matter" was a stand-in term for something unknown that seems to contradict what we know about how gravity works at large distances.

Cosmologists will tell you more but it doesn't contradict how gravity works at large distances at all - we just see gravity working on something in a familiar way and don't know quite what it is.

Actually, I think, we take it as if it's the gravity we know at work. We deduce the distribution of dark matter using the premise that dark matter is governed by the same gravity law.

If the distribution is actually different or if there's something entirely different, but with the same observable effect, then...