The two biggest problems for Dawkins' and Pinker's interpretation of what the gene means as a heritable "element" that affects phenotype. Is that first it is most often not an element but a system of non-local and interacting elements and secondly and most importantly it will not follow Mendelian genetics. It will not be segregating and discrete. There will be a myriad of variations depending on how the system responds to the environment it finds itself.
Mendel was lucky with the characteristics he chose to examine and when you do have genes that segregate then you do have a gene as described by the molecular biologist and geneticist, of they type that Pinker riles against. They are just different alleles corresponding to an expressed region of DNA or possibly their cis regulatory regions. They are not the nefarious and indeterminate objects defined by Pinker and Dawkins. If we are to take their views seriously then we have to go back to before the modern synthesis and try again.
Now that we know that most of the genome can be defined as loosely functional, even if just in terms of spacing between coding regions, then perhaps we do need to look at what the term gene means.