My answer must naturally be dependent on my own opinion about what a martial art "is." My opinion disagrees greatly with yours, so take the answer with a grain of salt.
The Tl/Dr answer is "absolutely, martial arts would be useful for such a creature." The full answer is a bit longer, and has to work its way up to the conclusion.
Before discussing martial arts, I'd like to start with what I will call "combat training." Combat training is, pure and simple, designed to teach you how to succeed in combat. When we teach soldiers how to ram someone through with a bayonet, that is combat training. It serves absolutely no purpose beyond helping a solider survive in war by killing the other guy before the other guy kills them.
The problem with combat training is that, like all training, it takes time and effort to become proficient in this. I don't know how to kill someone with a bayonet. It's never been worth my time to learn this skill, because the probability that I will ever find myself in an environment where I need to oppose someone with a bayonet is so astonishingly small that I can't justify spending hours to learn how to do it right.
Martial arts attempt to answer this issue by finding ways to make the training worthwhile to those who can't rely on a steady stream of war to validate their training effort. They seek to find ways to teach this art of combat in a way which also provides benefits in daily life. It's well known that people take up martial arts to build confidence, but that confidence doesn't truly come from knowing that you can beat up the other person. It comes from developing a skill set which they can confidently apply in real life situation.
I have some level of proficiency in the sword from my school. In theory, that means I should be able to kill you with a sword because you haven't practiced it and I have. In reality, I never expect to actually reach a situation where I have to use a physical sword to attack someone. However, the way my school teaches the sword also teaches me how to use other sword-like things. It is oft said that the pen is mightier than the sword. In business negotiations, written and spoken words are often as sharp as swords. The way my school trained me permits me to wield these words analogously to how I would wield a sword. Thus, by teaching me how to get what I want by using a sword, they also teach me how to get what I want using words. Far less bloody!
user54373's argument that martial arts largely stem from poverty can be viewed through this lens. Many who were poor could not afford weapons to defend themselves, or were forbidden from owning them. Martial arts were developed as a way for those people to defend themselves, but the poor can rarely afford to spend their time learning to defend themselves without getting some other benefit. Thus you see martial arts which leverage techniques seen in clearing fields. You see martial arts which leverage dance. You see martial arts which leverage any aspect of a poor individual's life that they can, creating ways to feed off their existing skill and to feed back into their life. It's the beauty of wedding this combat skill into one's daily life that earns "martial arts" their "art."
So, from this perspective, it's clear your intelligent quadrupeds would naturally have martial arts. It has nothing to do with having built in weaponry like claws, or built in armor like thick bony plates. It has everything to do with needing to take the training required for combat and fit it into a lifestyle which has value in peacetime. If your intelligent animal has times of conflict and times of peace, martial arts will have a place in its life.