TimedMediaHandler's use of jQuery UI adds a set of additional loads to any page that has timed media on it. This is (a) ugly and (b) expensive in terms of client time/network/CPU.
Instead, let's use OOUI's styles, which are arguably not better but are at least consistent, and don't need additional loads (as right now many, and soon enough every, page load already loads this).
Note that we are also considering dropping those parts completely as part of T100106.