...you may not copy, modify, translate, distribute, transmit, publish, republish, perform, display, post, download, upload, frame, make available, lend, hire, communicate to the public, adapt, or sell the FunSockets Content or any portion thereof.
Now, I'm not sure, but this looks to me like it would stop videos. I mean, post it, anyway. Maybe not record it. But somehow YouTubing the stuff seems like it would be distributing, transmitting, publishing, repubishing, displaying, posting, uploading, making available, something that is a portion of their content. Certainly communicating it to the public.
I especially think that it looks to apply due to:
With the exception of third party materials and user-generated materials as addressed below, all content available through the Service, including without limitation text, photographs, images, graphics, designs, audio, video, games, applications, software, and files ("FunSockets Content") is the proprietary content and property of, and is solely owned by, the Company.
Now clearly, the videos are user-generated, but they're using the site's stuff. So I don't think they'd qualify for this exception. Especially as if you read the pertinent part 'below' where they 'address' it, it seems to just refer to things that you post to their site, not stuff which in any way originates from it.
You may use the Service solely for your personal, noncommercial use.
This is a little bit that way too, but very clearly against any commercial gains of someone. Such as, like, (oh my, I sound like Ms. Teen South Carolina...), monetizing a youtube account these were posted on. I know people DO stuff like this all the time, but I'm very conscious NOT to.