They most certainly do. And it most certainly is.
Other than the fanciest Vegas restaurants, the nightclubs are the only venues in the city that enforce a dress code. But even if they didn't have one, especially if you're a guy, you're going to spend an awful lot of money to try to impress a well-dressed woman, so you have to look the part.
Also, when the general admission line is hundreds long, the door guys are looking for any excuse not to let people in. If you're not properly dressed, you'll never pass muster.
For guys, this means "business casual." And that means you don't have to (or want to) wear a necktie, but everything else should be about business -- as one writer put it, like you're applying for a middle-management position: a tucked-in collared shirt with buttons, dress slacks, and dress shoes. No workout clothes, jerseys, jeans, baggy pants down around your knees, tennis shoes or work boots, and definitely no hats.
The girls generally don't need to be told what to wear or not to wear, but just in case. Little black cocktail dresses are the uniform of choice, the more skin the better (as far as the club is concerned). Ultra-chic or at least currently fashionable dresses are also acceptable, if they're sexy. Same goes for the shoes. The more you can look like a Victoria Secret model, the more popular you'll be.