That way it's easy to compare different opinions and see who was "more right".
Throwing out percentages without methodology and test data bolstering that methodology amounts to persuasion.
It really opened my eyes to how illusory the utility of the percentage was - if it can flip that hard that fast, clearly it was never really only a <5% chance of happening, and the guesser really didn't know anything meaningful. It's astrology for the educated.
The labeling on the horizontal axis on the chart is terrible, but roughly this is a change from 20% to 95% in about 2 or 3 hours. It doesn't look like they ever had it at less than 15% (again, give or take a few points due to bad infographic-esque picture).
Did that really happen? The numbers I remember before the election were about 67% chance of Clinton, though I don't recall the NYT. On election night, I recall Clinton not doing well from the start.