If you experience an infinite update / download of the game in Steam, please, try the following:
1. Pause the game download in Steam.
2. Find the War Thunder folder, and rename it (e.g. "War Thunder1").
3. Uninstall War Thunder in Steam library.
4. Rename the folder back to its original name.
5. Find War Thunder in Steam client, and click "Install".
6. Steam will verify files, and download the missing ones, if necessary.