Never heard about Moves but it seems to record everything, send it to their server, analyze it there, then send you that notification. So, they know it's being used.
Yes you are correct. Reading the built-in help of the Moves app show the data collection end up on their server... So they clearly know which user is still running the app. If users were to disable pushes and no more daily data collection was happening then Moves will know they lost one user, but stating they don't know as the article show is a wrong conclusion.