What may be important to remember is that the author of Gen.9 (P) had previously described in 8:20 a distinction between "clean" and "unclean" animals. Generally speaking for P what was clean for Jew to eat was clean for YHWH to "eat" via sacrifice. Therefore Gen 9 must be read in context. The story is an etiological legend about the prohibition of blood. There is no reason to assume that the author here was suggesting that literally every animal was clean for food but rather that animals of many varieties would now serve as food as various kinds of plant matter had previously. The same author/s that wrote this section wrote Leviticus. The author when writing this story had in the background the then existing code in Leviticus and did not feel the need to describe it again at length in this short story.
Ultimately the Bible has a number of differing opinions about food prohibitions reflecting differing views of propriety and holiness. So yes the WT does imitate the Bible in this regard, it changes with the times and tides of opinion.