The War Room - Battles
The Battles subscreen in the the War Room is where you can form new games, join existing games, or check on the status of games-in-progress.
You get to the Battles subscreen by pressing this button:
The left panel continues to accept and display chat for the Gathering you are presently in; the right panel shows a list of battles presently forming or in-progress. The button on the bottom of the battles list allows you to form your own games. Pressing it brings up the Host screen.
Clicking on a battle in the Battles list will bring up a window with the current stats for that battle. If the battle is still forming you can join that battle if you want, or return to the War Room. If the battle is in-progress you will see the stats for that battle, including the number of units killed by each side.