Yes you're right, the overall process of a plant growing and then the plant dying and breaking down is carbon neutral. Sequestering the carbon would interrupt this process and make it carbon negative. This is generally speaking a Good Thing since so many other processes are carbon positive.

There are currently many efforts around the world looking to ramp up biochar production and use in remediating agricultural soils. For example, in many places after harvest time, leftover wheat stalks are gathered up and burned to get rid of the waste. This creates a lot of smoke and air pollution. Some companies are instead picking up the waste, transforming them into biochar and then tilling it back into the soil. https://farmland.org/biochar/

A Spent Coffee Ground project could be analogous to this.

What further puzzles me is how they decided to use coffee. Surely there are many other waste products that have the required structure. Is coffee the first thing they tried?

Could probably also use other sources of biochar. Since you're replacing sand, it may be an advantage that the coffee grounds are already ground up very finely. I'd imagine something like wheat stalks or corn cobs might be too large to replace sand and require further processing.