Hi John and thanks for getting in touch!
The Events Calendar does indeed have an upcoming events widget that can be used to display a specific number of future events from the calendar.
To get it looking exactly like that would take a bit of custom development. We have a Themer’s Guide that provides the ins and outs of how to customize any and all of the plugins’ templates that I would recommend checking out.
Speaking of nonprofits, we do have a program that I would encourage you to apply for as well. If qualified, you can get a free license to either Events Calendar PRO or Event Tickets Plus. Here’s more info on how the program works.
Does this help answer your question? Please let me know. 🙂
Cheers!
Geoff