Well the definition is correct, it is Antagonistic's narrow interpretation of that definition that is incorrect.
The key is evolution. For something to evolve, it must have the ability to be transferred, to be changed/mutated, and to be stored. Both genes and memes have these properties.
Literally any idea is a meme. If you can think it, it's a meme.
If you break a gene in two, the result is two genes. If you break a meme in two, the result is two memes.
The name "Antagonistic" is a meme. The letter 'A' is a meme. The sound you make when you say 'A' is a meme. The idea of air vibrating to make sound is a meme.