How do I display category items in a view content pane?
Try this...


In your view that displays movies and plays, add the term id (tid) to the list of fields. 
Rearrange your fields so that the tid field is above the term name field. 
In the tid field settings, check Exclude from display.
In the settings for the term name field, check Rewrite the output of this field. In the text box underneath, enter this:

&lt;a href="path-to-page-with-content-pane/[placeholder1]"&gt;[placeholder2]&lt;/a&gt;


Expand the Replacement patterns section of the dialog box to see what to insert in place of placeholder1 and placeholder2. Click Apply to close the dialog box, then save your view.

Now, in your content pane view, you simply have to match up the contextual filter with the tid. One way to do that is in your contextual filter settings, click the Provide default value radio button, select Raw value from URL from the dropdown, and set the path component to match where placeholder1 appears in the link generated in your other view.

This is the simplest way to do it and it has some limitations (e.g. a non-intuitive Url) but hopefully is enough to get you on the right track. One you're comfortable with it you can experiment with different arguments and different ways to pass them. The link below has a good description of how to use contextual filters:

https://www.metaltoad.com/blog/using-drupal-contextual-filters-views