It's the definition of any distributed system (or even single server) where you can deploy code, whether it's Erlang or a kubernetes cluster you setup.

Is pushing new code for your server to run "arbitrary code execution"? I guess we can call it that. Is it an exploit?

Depends if the code comes from some random person on the internet from mechanisms that you don't intend for pushing new code to run (e.g. through a buffer overflow on your server or XSS), or if it comes from yourself through your official mechanisms.