No. Natural selection happens at the level of the phenotype not the genotype. Anyway a gene is not a piece of DNA, but a unit of heredity.

The reason why epigentics is less important in evolution is because it is unstable. If an environmental factor can shift the phenotype one way then another factor can shift it back. Most of these unstable epigenetic changes wash out in an evolutionary short time frame.

Not sure why this is being downvoted, but it's definitely the case that as we learn more about epigenetics, we will need to modify our understanding of evolution substantially, particularly the relationship between epigenetic expression and mutation, in which the latter can "lock in" the changes from the former and lead to more rapid speciation. Exciting stuff.

I think the existing understanding of evolution is still fine. Darwin wrote,

1.More individuals are produced each generation that can survive.

2. Phenotypic variation exists among individuals and the variation is heritable.

3. Those individuals with heritable traits better suited to the environment will survive.

4. When reproductive isolation occurs new species will form.

When Darwin proposed this, he didn't have any idea of molecular genetics, let alone epigenetics. Mendel too wrote about alleles but he didn't know about base pairs of DNA. Evolution really only concerns phenotypic variation, not the underlying basis for it, so it doesn't matter if the variation is due to a genetic or epigenetic change.

People like to get carried away with epigenetics. It's not a revolution in our understanding of evolution. At least not at this point. The Darwinian model still explains basically everything you need to know about evolution. Epigenetics (by which I mean environmental changes to germ line DNA) is what software engineers would call an edge case.

Epigenetics and horizontal gene transfer: https://en.wikipedia.org/wiki/Horizontal_gene_transfer