I bet it's just in the metadata or part of the container file at worst. Meaning, you could extract the video stream and audio stream and then remux them together to be free of it. All without having to re-encode anything.
Though, it wouldn't be impossible to re-encode just a single keyframe length's worth of video with a digital watermark for every user who downloads the video at excogi. I've never heard of a site going to the trouble of doing that, but it certainly could be done. For example, with TMPGEnc Smart Renderer or software that worked similarly.
Or, is it that excogi's player can't be downloaded from at all, and the player is adding a visible watermark for each user that can be seen in screen recordings.