Is wrestling considered a martial art?

That depends upon the definitions. For the majority of the world, all Martial Arts are lumped together.

Some of them are trained as sports. Most of the Modern or Mixed Martial Arts (MMA's) are practiced as sports. The martial arts in the Olympics, Judo and Tae Kwon Do are sports with rules and limitations.

The traditional practitioners continue to teach and learn the martial arts as a way of life and a way of combat.