You don’t really need to know the exact geography of the area to be able to navigate in the city.
The New York City Subway Map Redesigned
Tommi Moilanen

However, omitting rivers entirely omits one of the most key points of orientation for people visiting the city. I lived in Manhattan for 2 years, and whilst I couldn’t tell you much about where Bronx, Queens, etc start & stop, I could draw an area map with the rivers and the island with my eyes shut. Walking around the city, that’s even more key (for me) as an orientation point than Central Park — and even if depicted geographically-inaccurately, it at least gives a way to orient yourself.