If I were building it, I’d do the watermarking on the individual assets & textures.
Your asset pipeline would publish these to the solution, which would pack it up ready for distribution.
Except, each beta tester logs into the game and the publishing system gives them a personalised set of assets with a unique noise filter thrown over the top.
Mr leaky beta player publishes a video or screenshot of the gameplay, and then the studio can just reverse the noise algorithm to get their unique ID.
Absolutely terrible for large scale content delivery. But for a small closed beta, probably not an issue.