With images and video, it's less clear exactly what they're doing, but it's watermarking on the pixel leve. From one of their blog posts:
Videos are composed of individual frames or still images. So we developed a watermarking technique inspired by our SynthID for image tool. This technique embeds a watermark directly into the pixels of every video frame, making it imperceptible to the human eye, but detectable for identification.
synthid used to be a waitlist-only tool but you can now check to see if images are made by imagen in google’s cloud console. You have to have a Vertex billing account to use it.