The idea involves lifting thousands or tens of thousands of blocks, not just one. Of course it's ridiculous to have an entire tower crane dedicated to lifting a single block, but that's not what they're proposing. The linked article has a rendering showing how many blocks are involved.
You want to use blocks that are as big as possible so you get more energy out of each trip. 2.4 tons isn't very much at all compared to the carrying capacity of a crane -- you want as heavy as possible while still being comfortably within the lifting capabilities of the crane. Their design says 35 tonnes and that does indeed make more sense. Where is your doubt coming from?
