Kite it claims to be xhtml but luckily it actually is not, because with that bad syntax, the final / missing before the close > in every link element etc then it would just completely fail in every browser because in real xhtml errors cause termination at that point with an error page in my experience. It is quite a general syntactical brokenness. Someone does not know what the rules for writing xhtml are but luckily does not know how to set up the server to advertise it as xhtml either so the two bugs cancel one another out with the result that the content is just html and a tag soup complete mess. The designers would need to keep using the w3c vaidator until the get zero errors. But as it is they are just winging it and while it seems to work in some browsers they are non the wiser. This is very very common, people seeing references to something called xhtml, thinking that it is somehow a good thing while not understanding it and so a complete dog's breakfast is the result. They maybe copy snippets of markup from somewhere, while not understanding them and then they just mix it all together.
The SMF core is fully W3c compliant for xhtml. Unfortunately where it breaks is when you add 3rd party code.
By 3rd party code I mean plugins such as official code supplied by Facebook, Google, Paypal etc.
These 3rd parties tend to supply generic code - rather than xhtml or html5 or html transitional etc specific code. If you search its the same 3rd party generic code that causes W3c issues for not just SMF, but other forum software and blog software such as WP.
Sometimes the site owner is able to amend snippets of the 3rd party code to stop W3c errors (I did exactly this with the paypal button), but others prove more difficult. Yesterday I spent an amount of time trying to resolve the google code but despite trying several suggestions failed. Time and time again I saw many frustrated website owners trying to find a solution for the generic supplied google code.
I reported the FB plugin bug yesterday and someone is trying to replicate this and find a solution.
Whilst they may be able to solve the bug why the videos aren't showing, there's no guarantee that they will be able to fix the W3c error, even though I have mentioned it.