How can one play War Thunder without STEAM?

According to the official forums, yes, many players have been doing just that for years.

It's also listed on List of DRM-Free Games on the Wikia -- under "Launcher-free Games" heading, though that just means it's not using Steam as a launcher.

And since it's not originally attached to Steam and Steam Cloud there should be no issue with the save data, whereas there could be if it was one of the games that needs modifying to run without Steam.

The easiest way to find the executable is to right click the game in Steam and go to Properties -> Local Files, as this will find it in any Steam Library Folder.

Then you can right click -> create shortcut and move that to your desktop, or wherever you'd like, and use that to start the game more easily in the future.