There are a few variants of this, most notably collegiate style vs. Greco-Roman style, but I think of it as a martial sport similar to Judo and hence useful for self-defense.
I don't really think of it as a martial art either. There is no mistaking it for karate everything that you learn in wrestling is to take an oppent down or imbolize him. There is nothing that you learn for the street, nothing you learn because it has been learned for hundreds or thousands of years. Not that this is bad in the street it will work out good a throw that you use in wrestling can be devestating on concreate or a firehydrant.
A fighting Style, does it teach you techniques that allow you to either control your opponent or disable your opponent from hurting you? Then it can be a Style of fighting.
What is a Martial Art? Something that teaches you a higher discipline? then this could also be used for this purpose as pointed out by Primo. Now, the question comes in, many people do not call an art that does not punch a martial art. I then reference Aikido and Judo. Are they a Sport or a Martial Art or a Martial Style of fighting? Now if you add in head butts, forearm slams and one inch punches with all the locks and take downs, then does this make wrestling an Art?
In My Opinion, Wrestling in any form is a Martial Art.