True, but I'd say not necessarily. The Reckoners are the Big Bad in Deadlands, but the sourcebooks have stated that there are ancient things that exist even apart from them (I'd reckon that the Cackler is tied to something like that).
As has been stated, most of the monsters/abominations in Deadlands are a product of the Reckoners, feeding off of people's fears to create new things to make people afraid. A local legend tells that there is a monster living in a nearby cave that eats children ... people fear the cave. In an effort to keep up the fear supply, the Reckoners create a monster to live in that cave that eats children. NOW the monster is real and it's everything that the people feared all along, BUT it doesn't mean that the monster that they feared has been there all along.
That being said ... if a Chinese demon is a real thing living in some corner of the spirit world (Hunting Grounds or otherwise), then that's one thing. But if a group of Chinese immigrants fear that a Chinese demon is tracking them down, there's nothing stopping a Reckoner from creating something that walks/talks/smells like the real thing to continue messing with them ... but it's not necessarily a demon from Chinese myth and legend.
In other words ... In Deadlands, if it walks like a duck, talks like a duck, and smells like a duck, it may just be a horrible abomination created by the Reckoners to strike fear into the hearts of people everywhere that just happens resemble a duck.
As the same time, real ducks do exist ... and it's certainly possible that some of the stranger myths and legends from other cultures are tied to real things that have nothing to do with the Reckoners.