The basics of the point-system you are wanting, isn't difficult. However once you get into them submitting links/videos/retweet-links; things can get a bit complicated.
I can get the full system setup, and testing within 1-week, for a flat $500. This will not be pretty, and will only have a minimalist design; this is for the programming, and display-systems alone. If you're interested in a customized design for this, I can do that as well; however you omitted design from the project outline.
I'll be utilizing PHP (backend), SQL (storage/data) and Node.JS (API); I can build this within Wordpress if you'd like, to simplify growth down the road; or I can build this as a stand-alone system. Either way is fine with me, I would recommend WordPress; so future development/design work is more readily available to you.