I would guess the first two lines would be a single line instead:

$EM_Event = em_get_event(get_the_ID());

I am not familiar with the coding of Events Manager. I do not know what they mean by the next line that they gave you:

echo $EM_Event->output('output your html with placeholders');

The text string output your html with placeholders is obviously meant to be changed, but to what I do not know.

Potentially you are looking replace all of this code in our template:

<div>
  <h2><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></h2>

  <p><br /><?php the_excerpt(); ?></p>
  <?php 
    if ( has_post_thumbnail() ) {
      echo '<p>';
      the_post_thumbnail("small");
      echo '</p>';
    }
  ?>
  <p><?php the_category(); ?></p>
  <p><?php the_tags(); ?></p>
  <p><small><?php the_date(); ?></small></p>

</div>

<hr />

Ah, the code needs to be inside php tags then, like this

<?php
$EM_Event = em_get_event(get_the_ID());
echo $EM_Event->output('output your html with placeholders');
?>

It should look more like this:

<?php
	while ($query->have_posts())
	{
		$query->the_post();
		
		$EM_Event = em_get_event(get_the_ID());
echo $EM_Event->output('<div class="event-listing">
<div class="event-thumbnail-wrap">
<a href="#_EVENTURL">
 <div class="event-thumbnail" style="background-image: url('#_EVENTIMAGEURL');">
</div>
</a>
</div>
			<div class="event-text">
               <span class="eventdates">#_EVENTDATES</span><br/>
               <span class="eventtimes"><em>#_EVENTTIMES Uhr</em></span><br/>
                <span class="eventlink">#_EVENTLINK</span><br/>
<p>#_EVENTEXCERPT</p>
   {has_location}<br/><i>#_LOCATIONNAME, #_LOCATIONTOWN #_LOCATIONSTATE</i>{/has_location}

           </div>
</div>');
	}
?>

BUT, the part in the output brackets may be problematic and it has single quotes around double quotes with single quotes inside. You may need to show that to the Events Manager support.