We should think of it like this - evolutionary theory describes how design is created by the competition between replicators. Genes are one example of a replicator and memes another. The general theory of evolution must apply to both of them, but the specific details of how each replicator works may be quite different.
This relationship was clearly seen by the the American psychologist Donald Campbell (1960, 1965) long before the idea of memes was invented. He argued that organic evolution, creative thought and cultural evolution resemble each other and they do so because all are evolving systems where there is blind variation among the replicated units and selective retention of some variants at the expense of others. Most importantly, he explained that the analogy with cultural accumulations is not from organic evolution pe se; but rather from a general model of evolutionary change for which organic evolution is but one instance. Durham (1991) calls this principle 'Campbell's Rule'.