I think something like this should work.
//Triggered after the slideshow has completed transitioning to the next slide.
$( '#mySlideshow' ).on( 'cycle-after', function(event, optionHash, outgoingSlideEl, incomingSlideEl, forwardFlag) {
$('video', incomingSlideEl)[0].play();
});
//Triggered just prior to a transition to a new slide.
$( '#mySlideshow' ).on( 'cycle-before', function(event, optionHash, outgoingSlideEl, incomingSlideEl, forwardFlag) {
$('video', outgoingSlideEl)[0].pause();
});