I think YouTube or Vimeo does not have (even paid) any longer API, that will allow me streaming with use of the progressive download the video files (MP4, MPEG-TS or even FL
In ASP or c# you can use below code, this will return you json string
string url = "https://api.vimeo.com/me/videos/" + videoId;
HttpWebRequest request = (HttpWebRequest)WebRequest.Create(url);
request.Method = "GET";
request.Accept = "application/vnd.vimeo.*+json;version=3.0";
request.Headers.Add(HttpRequestHeader.Authorization, "Bearer YOUR_ACCESS_TOKEN");
HttpWebResponse response = (HttpWebResponse)request.GetResponse();
Stream resStream = response.GetResponseStream();
var reader = new StreamReader(resStream);
string jsonResponse = reader.ReadToEnd();