The modern understanding of Darwin's theory (even the original theory, not necessarily neo-Darwinian extensions of it) apply to the origins of life and non-biological systems as well. Darwin himself was largely concerned with biology and restricted his published writings to that topic, but even he saw the application to the origin of life, and implications for religion. Even if he hadn't, we generally still use the discoverer's name to a theory even when applied to a domain outside their original area of concern.

The term "survival of the fittest" predates Darwin's Origin of Species, and was adopted by Darwin within his lifetime, btw.

The term "Darwinian evolution" applies to any process that comprises iterated replication with random mutation followed selection for some quality metric. Darwin himself would not have defined it that way, but he still deserves the credit for being the first to recognize and document the power of this simple process.