[walrus01]

Many commenters are pointing out that one possible definition of a rootkit is something that elevates privilege, but does not necessarily have network communications functions or a command and control server. But in recent times, almost all modern rootkits seen in the wild have some form of network control functionality.

[woodman]

A rootkit isn't for privilege escalation - you need root before you can install the rootkit. This is typically obtained through a privilege escalating exploit, the rootkit is for maintaining access and masking the attack.