If it works here but not there, something in your site configuration has to be different. The link https://vimeo.com/65107797 also works on my Digital Ocean hosted Discourse, which I just updated to absolute latest to make sure. I also made the post in the staff category to match your private post example, not that it should have mattered:
I wonder what the configuration difference could be, since it works here on meta, on try, and on my self hosted Discourse just fine?
It is possible vimeo has blacklisted your server or your server IP ranges. One way to tell this is the case, is if other video oneboxes work fine (youtube, etc) and other types of oneboxes.