Should it be "Just like any other type of martial art"instead?

Yes – it shows that karate is, itself, a martial art. Compare:

Just like any type of martial art, bicycling is a good cardiovascular workout.

Maybe better as

"Like most martial arts, karate is..." (etc.)

This says that karate is one of the martial arts, which include kungfu, judo, aikido, Tae Kwon Do (which is not karate), kyudo, jiu jitsu, etc., that is generally good for a cardio workout.

"Most" is better because much of the physical work in a class depends on the teacher's training methods more than the art itself. Some teachers don't do much that involves cardio.