I'm running into a similar problem, http://bugs.winehq.org/show_bug.cgi?id=23058 If you're using a different activex control, please file a new bug, with a way for others to reproduce the problem.
Any chance you could add an HTML5 mode? http://praegnanz.de/html5video/ shows a bunch of HTML5 video player components, and lists which ones have Flash fallback for old browsers. You could turn it on if you detect a Linux client, and otherwise use the old activex solution.