Ironically enough, Metal Gear Rising: Revengeance videogame from 2013 had a villain character who went on a monologue about memes, and a lot of people were confused by the way he used that term. But he described that original Dawkins definition really well.
> We are all pawns, controlled by something greater: Memes. The DNA of the soul. They shape our will. They are the culture — they are everything we pass on. Expose someone to anger long enough, they will learn to hate. They become a carrier. Envy, greed, despair… All memes. All passed along.
Yup. It's not a coincidence that it sounds like "gene". The idea was precisely to treat it like that - memes get passed from generation to generation, get mutated, mix with other memes.