Hard to say without more context but probably it comes from a "deep ecology" perspective. For example, a forest will suffer if you introduce some kind of pollution into it. Not necessarily just sentient beings, AKA animals, but all living things in the forest. So don't "cause suffering" to any of these living things because they are all intrinsically interconnected via the ecology of the forest as a whole. But of course, that does not meant that you must avoid walking on the grass, etc.
Another example would be to say the Earth "will suffer" because of global warming, etc. But of course the earth is not sitting here thinking "Ouch, that hurts!" because the earth itself does not think thoughts, have feeling, etc. But nonetheless, the earth will still "suffer" from global warming. From a deep ecology perspective, the earth as a whole, is called "a being", not necessarily in the literal sense of the word like "human being" but as one big interconnected system where each individual part is important to it. The living things that make up the whole are sentient beings and non-sentient beings, so don't harm either. Given the fact that the book is titled "Buddhism and Ecology", it's probably coming from this "whole system" ecological perspective.