You're lacking imagination. Given a library of GPU-optimized code for inserting these watermarks, a game absolutely could watermark the final rendered images before they're sent to the display. They wouldn't even need much information - just your license key - and it wouldn't need to be entirely recoverable from just a single frame.
The main tradeoff game makers would face is that this, like their other DRM, could be removed by skillful crackers who knew to look for it. However, if the game makers are sufficiently motivated, perhaps they could embed the information in more subtle places, like various game textures during loading time. This would also make it less impactful on framerates.