[рони]

noid,

playlist();

	$(function() {
	var currentVideo = document.querySelector('.play');
	var paused = 'paused' in localStorage;
	if(paused  == 'false') {
	  currentVideo.play();
	  $('.video-control').addClass('video-control_active');
	}
	$('.video-control').on('click', function () {
	    $(this).toggleClass('video-control_active');
	    if (currentVideo.paused) {
	        currentVideo.play();
	        localStorage.paused = 'false'
	    } else {
	        currentVideo.pause();
	        localStorage.paused = 'true'
	    }
	})
	});

заменить на

if(localStorage.paused !== 'true') playlist();
    $('.video-control').on('click', function () {
        $(this).toggleClass('video-control_active');
        var currentVideo = document.querySelector('.play');
        if (currentVideo  && currentVideo.paused) {
            currentVideo.play();
            localStorage.paused = 'false'
        } else {
            currentVideo.pause();
            localStorage.paused = 'true'
        }
    })