Does it? I don't understand this, at all.
More available housing would also create more demand, no? More people online will see the lower prices and move to Manhattan, immediately increasing the price again, no? The situation is complicated. You can't just say "supply and demand" and think you've solved NYC's problems in housing.
ECON textbooks teaching students that every person is a financially rational actor and that supply + demand plays out real nice in the real world is supper dangerous. My econ textbook was wrong in a lot of ways and it's upsetting to see continuing oversimplification and massive condescension for these antiquated and not-real-world-tested perspectives on how to solve complicated urban problems.