This makes no sense.

Why would non-profit applicants be competing with for-profit ones? Surely they'll be separate pools.

Understand your point, though to my knowledge YC doesn’t release numbers related to counts of nonprofit applicants. Might easily be even more competitive than the for profit applicants since would only take 60 nonprofits per batch to be at least as competitive as the for profit applicant pool.

More importantly: Are there partners focused on nonprofits? Do the batches have enough nonprofits to cluster like nonprofits? Is there training that’s specific to nonprofits? Do they have a demo day specifically for nonprofits? Is there a nonprofit alumni network with 10,000+ members? Does YC have a significant brand within nonprofit funding community? How many significant nonprofits have been a part of YC? Etc.

No idea why you're getting down voted. I was genuinely baffled myself. How do you run a startup (a for profit business?) that fights modern day slavery?

What's the businesses model here?

Number of aspects to nonprofit models. Funding wise, options include: donations, grants, loans, endowments, government contracts, for profit activities, for profit partnerships, government subsidized, etc.

Basically, much likely for profits, there patterns which provide insights into paths which are most likely to provide significant opportunities for growth.