My understanding (and some points in https://en.wikipedia.org/wiki/Chan_Buddhism echo it) is that Chan/Zen Buddhism is a descendant of Mahāyāna Buddhism and Taoism. In that way, it is itself a Taoist religion.

> Most of his other "translations" from ancient languages were made the same way as with the Tao te ching

This is incorrect for any Ancient Hebrew or Greek works. Genesis is listed as "translated". On the Psalms he says:

  I have translated fairly closely where that has been possible; but I have also paraphrased, expanded, contracted, deleted, shuffled the order of verses, and freely improvised on the themes of the originals.

From Googling "does stephen mitchell know ancient greek"

  Some of his translations aren't, strictly speaking, translations, but adaptations. He knows Greek, Latin, Hebrew, French, German, Italian and Danish, but he's also rewritten works in languages he doesn't know—Chinese, Sanskrit and Babylonian.