Generally, we instead have animal welfare laws that protect various animals to various extents for various reasons, based on human interest in said animals (e.g. You can sterilize any cat you find, unless it's owned by someone else, but you can never shoot a cat; you can shoot many wild animals within certain limits, but you can't sterilize them outside very special circumstances).
This seems roughly in line with how we treat certain wild animal populations though.
The same priority on property rights applies to trees. I can't cut down a tree on your property, but I can cut down a tree on my property. The town in the article made a assertion that is no weirder than corporations being considered "persons" with "rights", yet that is widely accepted in our society.
In fact, corporate "personhood" is even weirder: This town did not make a law to enforce trees rights. However, applying "personhood" status to corporations is written into law all over the place even though corporations are a human construct, not sentient beings. So, again, the only way the current laws are logical is to see that they are all about enforcing property rights, not out of concern for trees, animals, and -- at one time -- humans.
The general point is that animal protection are almost entirely subsumed to human rights - animals are protected in so far as their protection helps humans in some way (either specifically, such as your chicken being useful to you so that no one else can kill them; or environmentally, such as elk being important for the health of certain forests). Given the human need to consume or displace other living beings, this is the only tenable moral position that can be held anyway.
Outside of some endangered species laws those limits on fishing are to support commerce around fishing.
My kids grew up with rats as pets, and in many ways rats are proven to be more intelligent than dogs. But rats and cockroaches are notorious for upsetting commerce. Would you go back to a restaurant you saw had cockroaches? Consequentially, they are less protected because they are seen as a nuisance.
And if you have ever seen an industrial scale pig or chicken farm, those animals are most definitely tortured -- all legally. Why? To support commerce and big industry.
It's complex because government contorts ethics to accommodate capital and industry. Morality also changes over time. These days many people who eat pork would not want to kill a pig unless it was absolutely necessary to their survival.
Our descendants will look at us the way we do our slave owning ancestors. Except worse, because we’re leaving trillions of images and videos showing the grotesqueness of our behavior towards other sentient beings treating them worse than the way our ancestors treated other humans they saw the way we do other sentient animals.