Dueling was a legitimate means of combat in Asia, as it was in Europe and other parts of the world. But the significance of martial art on a grand scale is questionable. I'll leave that to someone with more readily available sources to touch on.

In China, martial art is one of the most important themes commonly found in literature throughout history and is a foundational element in today's Chinese society.

Take four of the most important literary works for example: Chun Qiu (春秋), Zhan Guo (战国), Shui Hu (水浒), San Guo (三国). Much of the writing was devoted to describing duels in great detail. It's simply not possible as a form of true witness account. But the imageries painted was meant to provoke feelings of good/evil, mastery, patience, etc, as evident from the fighting forms the characters took.

Over the past several hundred years, martial art has transcended beyond a merely embellished version of fighting. It became flat out fantasy in most aspects. One such common themes is "qing gong" (the martial art of lightness). This is basically all the flying stuff you see in Chinese movies. While it's for entertainment purposes, it has since reached the status of mystical. There are actually people who believe ancient Chinese masters used to be able to jump several stories high in the air.

In today's China, a lot of movie budget is dedicated to martial art films, such as Ip Man. Among others, martial art is used to show the strength of the Chinese will and character in face of more externally powerful foes. It's more of a motivation than historical recounts. Ip Man is just the current "star". There were many others that held this position, such as Huo Yuan Jia.

In addition, there are daily shows (ping shu) that is literally just a person reading martial art novels. It doesn't have to be martial art novels, but it general is. All schools also have mandatory exercises that take a lot of cues from the fabled fighting forms. Even old people will practice sword waving in the mornings as a way to stay healthy.

So, is martial art important in Chinese history? Absolutely, just might not be in the way you are expecting.

Well, this really depends on what you call a martial art. Chinese MAs as they are taught in most places are pretty damn far removed from actual historical practice, which included less backflips and more sparring. Modern Wu Shu is far removed from reality of actually killing people with swords/bare hands/whatever you happened to get your hands on by now, in all aspects, starting with equipment and ending with actual technique.

That said, there were MAs in China that worked, and worked well - we have some translated manuals of them finally seeping in (e.g. Military Preparation Manual), and there are beginnings of what is basically a Chinese HEMA - a movement that wants to reconstruct the methods of fighting and is concerned with their historicity and utility.

MAs that work are always very relevant to any society that isn't utterly pacifistic (so, any real world society) - it's what you teach soldiers. There's not that much difference between techniques taught to US Marines (MCMAP), medieval knights (Fior di Battaglia), Chinese soldiers (Military Preparation Manual) and samurai (Book of Five Rings). Most major differences are dictated by focus (less hand to hand for marines, because assault rifles cause it to happen less often) or by equipment (India has less thrusts in their saber techniques, as tulwars aren't best stabbing sword).

Last point is that if you want your MA to stay relevant, you have to absorb other styles into it, or at least develop things to counter them, so it will change over time. A guy out in the field doesn't care one bit about the purity of his style, he cares about not having a dagger shoved into his ribcage. Tracking what one style absorbed and what it developed is notoriously tricky - we are pretty damn sure that Japanese and Europeans invented Halfswording independently, but with countries that are not quite so far away from each other, it gets tricky.