Given the way it's written, I would say that technically, the first one with OF is right, provided "THE disdain of some of his ministers" is also used. However, it's a strange sounding sentence this way. The expression is "to have disdain for someone/something" or "someone disdains someone/something". So it almost sounds here like it's the video, a non-person, showing disdain and that doesn't work in English. Here are some correction suggestionsː a) Furthermore, that video shows the disdain that some of his ministers have for other institutions. b) Furthermore, the video shows that some of his ministers have disdain for other institutions. c) Furthermore, the video shows that some of his ministers disdain other institutions.

OF is correct. But I would rephrase it as "some of his ministers' disdain for other institutions," because that sounds more natural to me. Hope I've helped!