Howdy Ginger,
I’m happy you like the look of their widget. That widget they are using is one of the advanced ones that comes with Events Calendar Pro. Simply installing Events Calendar Pro on your website, and adding the “Minical” widget will give you that same look.
That said if the only thing you want from Pro is to change the look of that widget, even in the free version you can manually modify the widget template if you know CSS/PHP. While you won’t get the many features of Pro or and its widgets, you could add something visual simple like that date box with a theme override. Details on how to create overrides are in our Themer’s Guide, but again it requires an advanced knowledge of CSS and PHP.
Does that answer your question?
Cheers!
– Brook