To use leaflet you need to first change the loading settings for the API. Since leaflet does not come with a tile set, you need to define your own. It should be noted that utilizing mapquest uses leaflet as the base API.
        window.scribblemaps = {
            settings: {
                baseAPI: "leaflet",
                baseLayer: "http://api.tiles.mapbox.com/v4/jonathanwagner.jjch84hj/{z}/{x}/{y}.png?access_token=<Your Token>",
                attribution: "© <a href='https://www.mapbox.com/map-feedback/'>Mapbox</a> © <a href='http://www.openstreetmap.org/copyright'>OpenStreetMap</a>"

        var loadmap = function () {
            var sm = new scribblemaps.ScribbleMap(document.getElementById('ScribbleMap'));

    <script src="//www.scribblemaps.com/api/js?callback=loadmap" async>

    <div id="ScribbleMap" style="width: 730px; height: 500px"></div>
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