Methane is produced by methanogens in landfills, methane is not really part of the carbon cycle. The cycle itself isn't self contained, so all the carbon dioxide and methane join all the rest in the atmosphere. We want to reduce any greenhouse gas sources as much as possible, whether it's "carbon neutral" or not.

They can't just use any type of sand for construction, beach sand is out of the question as it's not rough enough. It's coming to the point that it's hard to find sources of sand that don't have negative ecological impacts, so replacing that component with something else is a good idea.

I'd be willing to guess that they already tested using bio char as a replacement and saw that it worked well in concrete, then started looking at waste sources of starting material that had sandy texture, then boom coffee grounds.

I mean, yeah, but isn't it carbon neutral? The coffee comes from the earth, returns to the earth. And couldn't coffee also be used for biogas?

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.