Singapore has a size of 728.6 km2, and a population of 5.7 million people. For a density of 8,400 people per km2. (That includes water reservoirs, military bases, an international airport, areas for heavy industry, nature reserves, garbage dumps, power stations, 1.5% of the world's crude oil refining capacity, a few semiconductor fabs, etc.)

There are 7.96 billion people on the planet. That means if you scale up Singapore at the same density, you'd need 952,000 km2 to fit everyone.

Texas has a size of 696,000 km2. So our mega-Singapore would need about 1.37 Texases of area.

That's pretty close to your number.

Wikipedia gives New York City's population density as 11,313.68/km2, but the borders for that calculation will by necessity be drawn a bit arbitrarily. And I assume that doesn't include as much of the support infrastructure as Singapore does.