Your understanding is great, Chaim.
It is forbidden to cause animals of different species to mate. Even though this is a commandment specifically for Jews, according to the Oral Tradition it applies to Gentiles as well. Tractate Sanhedrin 60a teaches that in reference to the verse Leviticus 19:19, the Torah's statutes regarding general laws related to the creation are also incumbent upon Gentiles, so that making changes to the original order of creation is universally forbidden.