The phrase originated as"run time" -- the time it took for an execution cycle "run" of a computer program or other event.
Over time it began being applied as an adjective in computer science, and thus became hyphenated, like: "run-time system" or "run-time execution".
As the word became more and more commonly used in computer science, folks started dropping the hyphen and now you'll usually just see "runtime". But it's not universal ... my browser spellchecker still thinks that's a typo :)
This NGram shows the relative usage of "run-time" and "runtime", illustrating the change in popularity in recent years.
To address Neil's comment below, consider this definition of runtime library from Wikipedia:
a runtime library is a special program library used by a compiler,
to implement functions built into a programming language, during the
execution (runtime) of a computer program.
And also consider the definition of execution/runtime:
run time, run-time, runtime, or execution time is the time during
which a program is running (executing), in contrast to other phases of
a program's lifecycle such as compile time, link time, load time, etc.