I am not sure that is fully true. Or at least not fully explained. The Steamdeck has a full KDE environment installed and it uses this when in desktop mode. But steam is not running in big picture mode in front of this.
KDE is not running at all when in the game mode of the Steamdeck. In that mode it uses a compositor written by valve called gamescope. Switching between these is effectively logging out and back in again to switch the compositor.
Also it now has a way to run the desktop as a nested session in game mode but that is winning kwin inside gamescope.