SproutVideo (http://www.sproutvideo.com) is already well established and probably their closest competitor as opposed to Vimeo PRO.
There are a ton of players in this space. Here are some others:
Edit: I'd also like to congratulate the founders of VidYard on their product. It looks great. Good luck you guys!
And Vively: http://www.vive.ly/
EDIT: Sorry, I noticed SproutVideo founder's list was missing SproutVideo; I failed to notice it was in the grandparent.