If you want to manage a Playstation, Xbox, Nintendo Wii you will need a ScreenCoach box, as it manages a TV and any connected devices.
Note that you can manually add sessions to a child's account, so you could look at device logs then add the time the next day.
If you have a Nintendo switch that is used without a dock, you can manually add session based on the data from the previous day's usage.
If you want to learn more about the ScreenCoach box please look at this FAQ:
https://support.myscreencoach.com/a/solutions/articles/51000361485