The two meanings are unrelated, they just happen to share the same word, probably since memes propagate in a similar way to memes. The "concept of meme" as informational analogue of genes is a thing independently of any other meanings the same word may acquire.
I use the term "memeplex" in order to differentiate it from what a meme is in the mainstream.
(Btw - I don't think the difference between "memeplex" and "meme" is substantial: It's a mereological distinction anyways. Similar to "Data" and "Datum").
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.
Now that I think about it, I wonder if that's why writers like to use words that are uncommon in general conversation. Since they're not used casually, they haven't been watered down and thus do a better job of getting ideas across to the reader.