According to me it would be really hard to rank a site with only videos and no text in google for any specific high competition term because
1) It wouldn't be clear to search engine what the motive of the site is and what category it belongs to.
2) There are thousands if not millions of websites trying to rank for keywords related to videos, and those websites do heavy SEO to rank for such terms. So, you will be at loss if you didn't want to provide nice long descriptions for the video and didn't keep em related to just one category.
You can maybe rank well if your domain is an exact match. Like, you own funnyvideos.com, then you can end up somewhere on page 3-4 .