I read the selfish gene back in 2006-7 ish, and I think that both the modern conception of meme and the original presentation of the idea fit rather nicely together and aren't contradictory. The more technical definition is broader, but non-exclusionary to the common usage. I think most people understand that the idea of meme goes beyond image macros: abusively quoting a moving to the point its devoid of meaning ('your father was a hamster and your mother smelled of elderberries'); cats (looking at you ancient Egypt); fart jokes (medieval art).
Memes that people call memes are memes. And some people recognize things more broadly and also call those memes. The definitions are nested and non-exclusionary, which is rather convenient.