I don't know if what that person wrote is true, but drains exist and it's not like Vegas gets a lot of rain, it's literally in a desert, floods aren't really a big concern.
There's an old book that I came across which basically discussed the architecture of Las Vegas and the small nuisance, such as titled sidewalks, that were crafted to maximize foot traffic.
Drains are typically between the pavement and the road to drain water from both of them no? Hence roads have a slight convex curve to them and pavements slope towards the road.
(it may have been this book https://mitpress.mit.edu/books/learning-las-vegas-revised-ed...)