OK, go ahead and reactivate everything to get it all back on track: thanks for working through that with me.
So I don't think this is a problem with this plugin. Here's why: even when it isn't running, the div that contains the individual events in the grid view is completely devoid of CSS classes.
Normally, each event within each table cell is wrapped in something called a div, and the opening tag (in a default installation) ought to look like this:
<div id="event_123-18" class="post-123 tribe_events type-tribe_events status-publish hentry tribe-events-event tribe-events-real-event cat_your-category entry">
Noting all of that class="..." stuff that is present in my example. This is the equivalent on your site:
Noting that there is no class attribute whatsoever. Off the top of my head I don't know what's stopping those attributes from displaying, unless perhaps the core plugin templates themselves have been edited, however the tl;dr is that this plugin won't work unless those classes - in particular cat_your-category - are present.
With that in mind, you would probably do well to pose the question of why they are missing over on The Events Calendar's support pages: