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You have two options to accomplish what you'd like in Wordpress -
1. Themes: You can utilize a content-sharing theme, typically available as a premium theme ($$), that includes functions such as user-submitted posts and voting/liking other users posts. Certain themes may require some code edits to be custom tailored for a video-centered website.
Here are a few themes that will achieve your goal:
I Love It! Content Sharing Theme - ThemeForest
2. BuddyPress: Considered the epitome of content sharing and social networking, BuddyPress is a plugin available for your Wordpress website and installs very easily. This will most likely require the most editing, but the plugin itself is free. Take a peek at BuddyPress' features on the latest Wordpress Twenty Twelve theme here.