What does it mean for ecocentrists to regard a tree or a fish as a moral patient?

I believe the correct answer is that we must care for these life forms for their own sake, and not just for the sake of how it might ultimately impact us.

Moral patients are objects/organisms towards which you feel moral responsibility. So, ecocentrists are obviously interested in the ecology and want to protect the natural environment, which is why they take care of nature in general.