"I don't agree, see my replies above"
I understand you disagree, but your rationale appears to be faulty.
"All animals do in fact have some moral standing."
On what basis do you assert thant?
"It is not OK to torture an animal, for example."
It is wrong to torture an animal because of the ill effect it has on "you" (the torturer) and possibly on others around you. This does not imply that the animal has any legal rights.
"Moreover, language and abstract thought are not requirements to have moral standing."
I disagree, on the basis that moral rules apply only in interactions with moral agents, and moral agency requires the ability to think abstractly (in order simply to comprehend moral obligations.) If you have a rationale for your contrary assertion it is not apparent.
"Elephants exhibit PTSD, for example. A young elephant that witnesses its mother being shot and killed will exhibit many of the same symptoms in later life that are associated with PTSD in humans."
And that relates to moral agency how?
Here's the point. Moral rules are two-way rules. I am expected to respect your rights, and you to respect mine. As long as we are both capable of understanding our rights and obligations that can work.
However, what if one of us is not mentally capable of understanding this? It would be absurd, in that situation, for one party to be expected to respect the 'rights' of a being who is not capable of understanding that respect or returning it.