The open and closed status is decided based on the current timing either the store is opened or closed, in the template the badges are not added by default but they can easily be added by copying the tags below and pasting them into the template either list or info-window.
{{if open}}
<li class="sl-opened"><i class="icon-minus-circled" style="color: green !important;"></i>[Currently Opened]</span>
{{else}}
<li class="sl-closed"><i class="icon-minus-circled" style="color: red !important;"></i>[Closed]</li>
{{/if}}You have to paste the above script into the ASL Settings > Customizer, by selecting the template you are using.
How it will appear on the front after applying the changes.