I also got to this page with an error, on iOS on iPhone 4 when using the Facebook application.
To play the video even if it has expired, find the message you want and instead of clicking on the embedded video, select the publication date. If the message reads:
John Doe shared a video with Jane Doe: December 1, 2012 at 9:30 pm.
... then you click the date and time on the post βDecember 1, 2012 at 9:30 pmβ and it will lead you to the video without using an expired link. The video should play like this.
Good luck.
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