E2E isn't a requirement for something to be called a backdoor, even though governments are constantly demanding E2E backdoors. An attacker having shell access

E2E isn't a requirement for something to be called a backdoor, even though governments are constantly demanding E2E backdoors. An attacker having shell access or a government getting plaintext dumps of whatever email conversations they want (when users don't expect it) are perfect examples of backdoors. AT&T giving the NSA a secret room for them to suck up all comms, encrypted are not, is also a classic example.