Energy consumption is a result of labor applied to tools and technology for production. It is not mere correlation, but it is also not the cause, it is one measurable downstream effect.
China, in fact, used energy consumption as the measure for GDP reporting. For this reason, local leadership in cities and provinces would game the system by running the coal plants at peak and turning on all lights in a city day and night to juice the numbers so they'd show higher GDP (Beijing used to do this before they hosted the Olympics, for example).