Maybe he's trying to go to the earliest idea of "gen-es" aka the reasons for the traits of an individual. The idea existed before the discovery of cells kernels and DNA right ? so in a way, if there are other mechanisms involved in passing traits to children, it could be termed as gen-something

Yes, that depends on the definition. Lamarck could fit into it, but he had no clue about DNA, genes and so forth; neither had Darwin. He babbled about gemmulae.

Even the definition of a gene is not very accurate. Many important sequences yield a miRNA or another RNA. Only few sequences yield a mRNA. Some "genes" are just integrated viruses/phages/transposons etc... that were modified. One of the most fascinating one was the retrovirus in regards to the mammalian placenta: https://pmc.ncbi.nlm.nih.gov/articles/PMC4332834/ but there are many more examples. We are all DNA hybrids at the end of the day. The whole species concepts makes very little sense these days, IMO. I can see the use case for eukaryotes, but it makes no sense to me for bacteria yet alone viruses.