This could be add-ons issue. Clear cache. Try with InPrivate window. Try to update Internet Explorer.
From Microsoft Support:
When you experience problems playing videos in Internet Explorer, these problems may be caused by a number of different issues. Most video playback uses Adobe Flash, Microsoft Silverlight, or Java, and these platforms require Internet Explorer add-ons in order to play. By making sure that you have the latest updates installed for Windows, Internet Explorer, and any Internet Explorer add-ons, you can resolve most video playback problems.
To troubleshoot video playback problems in Internet Explorer, follow these steps. Test the playback behavior after each step until the issue is resolved.
- Update Internet Explorer
- Test the video in Compatibility View
- Make sure that add-ons are installed and enabled
- Update to the latest add-ons
- Turn off ActiveX filtering and Tracking Protection
Seems this is a known issue, and Microsoft working on it. So troubleshoot from yourself and if still doesn't work, contact to Microsoft. This is nothing have to do with Twitter.
Have a look on these thread for more info: