https://en.wikipedia.org/wiki/Criticism_of_evolutionary_psyc...
The Selfish Gene is an excellent book with a lot of great insights, but it's not just "dated". It touched off a lot of really bad evolutionary psychology, full of fables that "explain" cultural features in biological terms. They are often without experimental evidence or poor-quality evidence. They're usually incredibly short-sighted when it comes to other cultures. Yet people often accept them blindly because they affirm their prejudices.
Before you go any further down the path Dawkins is pointing, I would strongly suggest you inoculate yourself with rational skepticism. Even scientists are prone to failing at that; it's the whole reason we invented things like peer review and replication.
Popular science books like The Selfish Gene are a two-edged sword. They can be great at introducing new readers to fields of science. But they risk misleading readers into thinking that they know more than they really do. That Wiki page is a jumping-off point into the potential failure modes of this particular science, which is widely misunderstood and over-extrapolated.
The Vital Question or Life Ascending by Nick Lane
The Gene by Siddhartha Muhkerjee