Hey there Argy,
The Battle.net application should pull information from the system on running tasks to verify if a game is on/off. If this isn’t happening it means something is blocking the app from reading system information correctly.
I might suggest checking over the system for anything that offers “Optimization” for the computer, or any type of security software. If any exist, disabling or uninstalling them temporarily may work to resolve the issue.
If you’re sure there is no background applications running, and the problem is still happening, we might need to try making a new administrator account to rule out any possible problems with the current user settings.