Hi. The free/core The Events Calendar plugin does add structured data markup. You can see it by visiting that link, viewing the page source, and searching for “ld+json”
FYI: I noticed console errors at your site. (If needed, you may reference our KB article Using Google Chrome Developer Tools.) I’d suggest getting those sorted out.
If you do want to upgrade to get PRO‘s extra features, we have a pretty great Refund Policy so you can buy one or many of our add-ons and thoroughly test them.
Let me know if you have any follow-up questions.