This diagram might help to explain the concept of the Gross Output first discussed in this post: A Triumph for Supply-side “Austrian” Economics and Say’s Law. The diagram shows the economy divided into its various stages of production. Adding them all up gives you a measure of the whole economy, not just the final output. Note that each stage is larger than the one above which indicates that there has been value adding activity going on.
The problem with double counting is massive if you are trying to measure final output. If, however, you are trying to work out the level of activity across every part of the economy, it is not the central problem, and this is especially so if you are interested in proportions. If the data were divided into where jobs were, the division between the different parts of the economy that took in the stages of production would make perfect sense. If we were trying to measure jobs and counted only those who were in retail and personal services, we would immediately see what was wrong with the stat. GO tries to make up some of the deficiencies in knowing only final output and ignoring the economy’s interior.