This is an outdated post.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.
Adversary: Embed Video 2 Answers