Ok in tests I got it working on my Wordpress site.
There are few issues.
The first one was what I said. Wordpress uses it's own JQuery plugin and apparently has a no clash policy on by default.
This means any jQuery plugin used by Hype will not be allowed to clash but Hype will not see Wordpress's JQuery.
The simple fix for this is anywhere you call JQuery using the dollar sign $ replace the dollar sign with jQuery
So for example
$(label).text( $(element).attr("alt") );
jQuery(label).text( jQuery(element).attr("alt") );
As @jonathan explains here:
When you are embedding as you are. Then you need to wrap the Hype Div in a div with a set size.
So make sure you use the full path to it
I assume it will be something like