This seems to work for now..
Added onended="onEndVideo()"
to the video element like so.
<?php $mrssfeed_url = get_post_meta(get_the_id(), 'nowthisearth_media_url', true);?>
<video onended="onEndVideo()" id="nowthis-video" class="nowthis-video" style="" width="1280" height="720" autoplay="true" controls>
<source src="<?php echo $mrssfeed_url ?>" type="video/mp4">
Your browser does not support the video tag.
</video>
Then did this for the javascript..
function onEndVideo() {
document.querySelector("a.next-post").click();
}