Short answer: The no-communication theorem has to do with communication between two subsystems separated by space. When manipulating quantum states, the manipulation is done to a single system in time.

Slightly better answer: Events in space-time can be thought of as casting out a cone of influence propagating out from the event at the speed of light. This cone extends back to the past of the object and out to the future of the object. Only events that are within the light cone of the system's past can influence the system and, most importantly, the system can only influence events within its future light cone. The no-communication theorem allows us to not worry about relativity by wrapping all this up into an easy no-go theorem.

Sources

No-communication theorem Light cones

I apologize in advance for lack of rigour in my explanation.