There are two answers to the questions. The first one is yes, you can watch videos on your Galaxy Watch 6 or Watch 6 Classic, but there is a condition. To play videos on your new Samsung watch, you have to stream it using Samsung Internet Browser. With the app, you can open YouTube, TikTok, Instagram, Facebook, Netflix, Disney, and other streaming sites to play or watch videos. Just go to any of the above websites, and stream them right from your wristwatch. You can follow this guide page to run YouTube on your smartwatch.
Now the second one is, can you watch videos that you have recorded or transferred from your phone? The answer is no, you can not watch those videos on Galaxy Watch 6. You will get unsupported file errors while playing offline videos. With Galaxy Watch 7 or Watch 8, we might have the option to play any videos, but for now, it is not possible to watch 1080p or 4K content on Galaxy Watch.