In this post we detail the steps involved to close background running app/process running on your Fire TV.
  1. Install Background apps and process list from the Amazon AppStore on your TV, you can do so by just saying the above mentioned app name in your FireTV remote voice search.
  2. On opening it lists various apps that are currently running in the background on your Fire TV. 
  3. Use the "Close all Apps" buttons, or "Close multiple"(Added in Dec 2018 Update) and close multiple apps with one button click, or,
  4. Select the app you want to close and hit force stop.
Additional Features:
  1. User can change the layout of the app by using the expand button(second from left) and selecting change layout.
  2. You can clear data/cache of the apps as you desire from application settings screen that appears on selecting an application listed.
  3. You can find the list of all installed apps including the system apps by using the expand button(second from left) and selecting All apps.
Things to note:
  1. Closing multiple apps at once works by closing apps individually skipping the need to select individual apps from the list, since Fire TV doesn't provide accessibility feature that enables developers to auto close apps on TV.
  2. Each app has to be force closed by the user, since Fire TV doesn't provide accessibility feature that enables developers to auto close apps on TV.