The easier question to answer is "Is it possible to track how many times a user clicked on a recording link?" as each click triggers an entry in nginx.
To actually know if a user is watching a recording is much harder. Nginx is streaming the recording (using pseudo streaming over https), but I don't know if there is any way to track this.
You could build a small client that embeds the HTML5 <video> tag (to view the recording) within the page and monitors the user's interaction with the tag and the corresponding bandwidth of the video stream (if this is possible). I don't know of anyone who has done this before.
Regards,... Fred