Most nonprofits don’t see themselves as competing with other organizations. In the traditional sense, they don’t. Most nonprofits don’t compete to sell a product or service.
Looking at competition in a different light, nonprofits definitely compete in a variety of ways with other organizations. They compete with other nonprofits and charities for donations, they compete with all forms of entertainment for the time of their volunteers. They also compete with significant industry lobbyists for the ear of politicians.