Suppose someone made a video to rally support for some project, but the video was poorly done and no one was convinced. I think I could write:
a. He failed on this video."
b. He failed at this video."
Should it be "at" or "on"?
I prefer 'in' or 'with'.
'on' video refers to the medium- or it used to, when video tape was introduced. Today, the term video has come to include all electronic media. 'The story is on video- not on film or live.' The content of the video is what failed, and content is in the medium.
Hard to imagine using at with video, unless the person did a very poor job of creating the video. 'He wanted to make a video, but he wasn't very good at it.'
Suppose, despite the poorly made video, he got funding for that project, but then made a mess of the project. I could write:
a. He failed on this project."
b. He failed at this project."
Would it be safe to bet my money on b) being correct?
I will go with "in" in your example.