It would be inaccurate, presumptuous, and perhaps even somewhat racist to say that martial arts belong exclusively to Asia. After all, the fighting skills developed and used by aboriginal Africans, Americans, Australians, Europeans, and Pacific Islanders throughout the course of history are also martial arts, and are not necessarily the inferior of any martial art developed in Asia.
It is true, however, that the heroic legends and stories of other peoples do not feature the same kind of martial arts as those depicted in Chinese wuxia stories.
The kinds of abilities attributed to wuxia characters are essentially superhuman: the most powerful wuxia characters can shatter stone walls with their bare hands, project concussive energy over extended distances from their bodies, fly through the air like birds, use melee weapons with a degree of speed and skill that seems impossible, heal grave injuries, etc. The martial arts of other peoples around the world, as far as we know, do not enable their practitioners to do these kinds of things. In European knight tales, for example, a knight who is a good fighter is merely stronger and better skilled at using his sword than are his opponents. He has no "superpowers" within his body, and any extraordinary or miraculous advantage he might gain is attributed to magic charms or spells given by fairies, wizards, or angels rather than a natural force than exists within his own body (and that he can learn to cultivate and manipulate through training and practice). The European knight is a martial artist of the first order, but his martial arts are not like the martial arts of wuxia fiction.
In Jin Yong's novels, no truly European characters appear other than Princess Sofia of Russia in DUKE OF MT. DEER, and she was no martial artist in any sense of the term. In Jin Yong's universe, "martial arts" in the wuxia sense seems to be limited to the continent of Asia. Surprisingly, Jin Yong allows that the reach of wuxia-type martial arts stretched as far west as Persia and as far south as India. A number of powerful martial artists in Jin Yong's stories hailed from Persia (i.e. Wan Hak Sai of ROCH and the Persian Ming Cult members of HSDS) or India (i.e. Lui Mor Singh of ROCH). Damo was from India, so Jin Yong probably had no choice but to concede that wuxia-style martial arts were practiced to a high level in India, but Persia was a surprise (Persia is geographically part of Asia, but the natives of Persia have more in common culturally and physically with the peoples of Europe than with the peoples of China and the rest of eastern Asia). One would imagine that as far west as Persia, there would be no practitioners of Chinese-type wuxia martial arts (with inner power, hing gung, etc.). On the other hand, Jin Yong did maintain a sort of Chinese or East Asian bias, often emphasizing that no matter how fantastic certain foreign martial arts were, they were ultimately inferior to Chinese martial arts.