“This is the only chapter in which I have not made my own translation, the one used being by the late Ku Hungming.”
Is it a typo or what, I simply just don't understand why there's a being there.
This is the only chapter in which I have not made my own translation, the one used being by the late Ku Hungming.
This means that the current author did not translate this chapter. They used the translation made by Ku Hungming. The last part of the sentence adds additional information. The subject of the participle being is the noun phrase the one used, meaning the translation that was used.
It could also be said in two separate sentences:
This is the only chapter in which I have not made my own translation. The one used is by the late Ku Hungming.
Here is a simpler example of the same structure:
I bought a new umbrella, the old one being in need of replacement.
This structure is described as gerund-participial as adjunct here:
Student's Introduction to English Grammar p.210
[11] i. She sought advice from Ed, [he being the most experienced of her colleagues]
[emphasis added]