It seems the usual way for the Project Management discipline to enter nonprofits is through their IT departments. Most if not all IT departments that generate software or arrange hardware installations have some level of understanding of Project Management tools and techniques. So the good news is that there is an avenue for Project Management to enter nonprofit organizations.
Unfortunately, I have heard and observed that only bits and pieces of the discipline make it out of the IT department. There appear to be some misunderstandings. For instance, moving post-it notes around on a wall is not Agile (a popular approach to managing projects, especially in software development); and, as one of my professors said to his students in the first class of my first grad school course, "Knowing how to use Microsoft Project doesn't mean you know how to manage projects". Using Kanban and project management information systems are useful tools for a project manager. However, execs who are initially introduced to them usually miss the point.
The central idea is to obtain business value by getting the most out of what you have, and if you don't have enough - to recognize that and decide whether it's worth it to get more or just can the project. There are many layers of skills needed to do that but unfortunately it seems most nonprofit execs only get a superficial introduction to cute tools rather than a full explanation of how to use Project Management to focus organizational energy like a laser in order to further their organizations' strategies.
Guess it's about time I make an article about the use of Project Management in nonprofits a higher priority.