Some values are not anthropocentric. I'm going to start with Karl Popper's epistemology. Popper points out that some knowledge is objective, it is instantiated in things other than human brains like books, computer programs, e-mails and so on, which means it can be criticised by others. According to Popper all knowledge is created by conjecture and criticism and can't be created in any other way. (In particular, it is not justified in any way.) If there were non-human aliens creating knowledge they, too, would have to create it by conjecture and criticism. As a result any thing that wants to create knowledge would have to adopt ideas that many people don't have, like the idea that you should answer criticism instead of ignoring it. This just leaves the question of whether there is some non-anthropocentric reason to favour the growth of knowledge. Imagine that there aliens or AIs or some other non-human thinking beings. We would have some disagreements with them and we would have to create knowledge about how to resolve such disagreements.
See "The Beginning of Infinity" by David Deutsch for arguments about connections between morality and epistemology and explanations about why rationality and science are not anthropocentric. For Popper's epistemology, see Chapter I of "Realism and the Aim of Science". For Popper's ideas on ethics see "Toleration and Intellectual Responsibility" by Karl Popper http://universaltolerance.org/articles/Toleration%20and%20Intellectual%20Responsibility%20%20Sir%20Karl%20Popper%20%20.pdf
and references therein.
Animals lack the ability to create new explanatory knowledge, unlike people. As a result there is a qualitative difference between animals and humans in that an animal can never make a contribution to the growth of objective knowledge in its own right. Dogs never learn to write, they don't learn English beyond some short list of commands, they can't write music or program computers. The reason is that a dog has a finite bag of tricks written into its genes and when it exhausts that bag of tricks it can't create anything new. Other animals are in the same position. For example, experiments in trying to teach apes language always reach a point where the ape can't do anything more sophisticated than what it already does. See "Kanzi: The Ape at the Brink of the Human Mind" by Sue Savage-Rumbaugh and Roger Lewin for an example. (See also "The Beginning of Infinity", Chapters 15 and 16.)
The animal has a particular set of knowledge (in the sense of useful or explanatory information) in its genes. So any copy of the relevant genes will have the same knowledge and no individual animal matters very much. By contrast, each person has a unique set of ideas and habits instantiated in his brain and that does matter. Every time a person dies unique ideas are destroyed that might lead to progress. Every time you mistreat a person you make it more difficult to get access to any good ideas he might have or that he might develop.
You might say that animals can suffer and so this provides another kind of value and that this value is not limited to humans.
An animal can't understand what is happening to it and so can't interpret the pain as being bad. The idea that something is bad is a sophisticated interpretation of experiences that only arises in the light of a lot of knowledge. For example, one reason people suffer is that they can imagine all the stuff they won't be able to do as a result of injury or death, unlike animals. Animals are robots programmed to propagate genes. To do this, genes program their vehicles to move away from stuff that will damage the vehicle, refrain from using damaged body parts so they can heal, signal danger to relatives and other stuff like that. They bear more resemblance to characters in a computer game than to people.
You might say that it looks like animals suffer, but that is an interpretation of what you see when you look at an injured animal. The explanation I have given criticises that interpretation. Likewise when you say an animal has a brain structure that is similar to some human brain structure you are imposing a false interpretation of what is going on. Both the human brain and the animal brain are universal computers: they can do anything that a universal Turing machine can do. It follows that you can't tell exactly what it is doing just by looking at the hardware. To the extent that some part of the animal's brain is similar to a person's brain it is participating in a very different process. The computation in the animal's brain doesn't involve understanding what is happening to it or anticipating problems as a result of an injury or anything like that: the animal doesn't suffer.