Theoretical biologist here. I’m going to push back on that just a bit. I think that you might have mentioned Selfish Gene, too. That was not the best book even at the time of publication (most biologists had a number of problems with it oversimplifying in a way that’s probably similar to what anthropologists think about Guns Germs and Steel). It also has been getting worse the more we learn.
Evolution acts on the phenotype, not the genotype. It affects the gene makeup of the population through differential reproduction rates. “Fitness” can be measured as a value relative to the rest of the population specifically by using the number of offspring. So what I’m saying here is that all factors that affect phenotype, whether genes or other factors, affect evolution.
So, of course genes are important. But you have epigenetic factors, too. link here You also have extensive non-coding regions that regulate transcription. You have rna editing. And so on.
If you’re interested, I would highly recommend a book called How Life Works by Phillip Ball. It was just published in November and is an outstanding summary of how much our understanding of life has evolved (heh) in the last 20 years or so.