I'm not 100% sure, but it sure looks like the shape is designed to result in equal strain/deformation throughout the structure.

Imagine the structure is sliced into horizontal layers. Each layer needs to support its own weight as well as the the weight of all the layers above it. Similar to the exponential effects of the rocket equation, this results in a rapidly growing mass requirement as the structure increases in height.

Some other towers actually have a similar shape, but with different constants at work due to their smaller height. Look at the profile of the CN tower: it also grows exponentially along its height.

Needs to be very wide as the base needs to support a 4km (2.5 mi) structure above it. It could be more narrow if you had no living space inside, but then it's even less useful.

For comparison the Burj Khalifa and Shanghai Tower also taper which dramatically reduce amount of weight the base needs to support. Further, if you somehow stacked them on top of each other that's still less than 1/2 as tall as this structure.