It isn’t disproven because it isn’t falsifiable. It doesn’t rise to the level of scientific theory, it’s a framework to understand cultural ideas through a biological lense. It’s basically “Check out this cool idea I had” level of rigor. There was a brief attempt to turn Memetics into a serious area of study but that died out.

Dawkin’s biggest achievement was writing The Selfish Gene, which presented an extremely good (Or at least extremely widely accepted) argument for a gene based view of evolution, which has basically become the assumed standard for most introductory biology at this point. There are many arguments against it that have been presented since, and gene centered evolution becomes less and less the standard the further your education goes, but it is what it is.