In this particular case, RCE means Remote *Command* Execution, not Remote Code Execution: an attacker can execute arbitrary commands with execv(), as root; no memory corruption or ROP (Return-Oriented Programming) is involved.

This vulnerability is exploitable instantly by a local attacker (and by a remote attacker in certain non-default configurations). To remotely exploit this vulnerability in the default configuration, an attacker must keep a connection to the vulnerable server open for 7 days (by transmitting one byte every few minutes). However, because of the extreme complexity of Exim’s code, we cannot guarantee that this exploitation method is unique; faster methods may exist.

source: solar