I'd actually say its current use is pretty close to its intended one. from the oed: A cultural element or behavioural trait whose transmission and consequent persistence in a population, although occurring by non-genetic means (esp. imitation), is considered as analogous to the inheritance of a gene.
1976 R. DAWKINS Selfish Gene xi. 206 The new soup is the soup of human culture. We need a name for the new replicator, a noun which conveys the idea of a unit of cultural transmission, or a unit of imitation. ‘Mimeme’ comes from a suitable Greek root, but I want a monosyllable that sounds a bit like ‘gene’. I hope my classicist friends will forgive me if I abbreviate mimeme to meme... It should be pronounced to rhyme with ‘cream’. Examples of memes are tunes, ideas, catch-phrases, clothes fashions, ways of making pots or of building arches. 1976 New Scientist 9 Dec. 619/2 A rational person who hasn't acquired any variety of the God meme described by Richard Dawkins. 1986 Canad. Jrnl. Zool. 64 1576 Congruence of the patterns of morphometric and cultural evolution in these islands suggests..that the differentiation has been influenced by a colonization history involving restricted gene and meme flow between archipelagos, subsequent drift, and possibly founder effects. 1993 Wired Feb. 132/2 I'm not sure what happens to such a culture when radical Maoism is replaced by the far more seductive meme of Western consumer culture. 1998 D. BRIN Heaven's Reach 27 On all other dimensional planes, memes could only exist as parasites, dwelling in the host brains or mental processes of physical beings.