This is an outdated post. Now it is possible to add videos to a Gallery Page: https://support.squarespace.com/hc/en-us/articles/208404698
Answer by Nate Miller · Oct 01, 2012 at 09:27 AM
You may want to review this thread: http://forums.squarespace.com/squarespace-6-forum/post/1750792#post1890279 As I understand it, this is on Squarespace's to-do list but not possible "out of the box" quite yet. It is however possible if you want to code it into place (again, see the thread above).
Hope this helps.