Eh. That's just exoticism. Western people tend toward this weird idea that their culture's historical fighting styles are basically just hefting big slabs of sharp metal or swinging their fists around, while everyone else has a deep and rich martial heritage that functions on a spiritual level and is incredibly complex and powerful and vaguely magic. It's a specific version of the whole "mystic east" cliche.
The reverse can therefore be surprising and a little amusing for us, like the bit in Sengoku Youko where the tiger-demon monk explains that he learned an exotic and powerful fighting style for the sake of overcoming his rival... and puts his hands into a boxing guard, immediately baffling his opponent with unusual footwork and crazy jabs. BOCK-SINGU!
If nothing else, Fate at least gives the nod to Pankration as the world's oldest known mixed martial arts style, which by the setting's rules should mean Chiron blows Shuwen's Bajiquan out of the water. Catch Wrestling has a deep folk heritage across Europe, which is what Beowulf's clearly exhibiting when he rips an ogre's arm off for the heck of it, so I don't see it falling behind Bajiquan except in terms of Nasu's middle school obsession.