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The chimney had a height of 195 metres and a diameter of 10 metres with a collection area (greenhouse) of 46,000 m² (about 11 acres, or 244 m diameter) obtaining a maximum power output of about 50 kW. However, this was an experimental setup that was not intended for power generation...
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Sun doesn't only hit the ground, buddy. It can impart energy to anything it does hit, which means the entire chimney is capable of heating the airflow inside. It's not just about the ground. The entire chimney also acts as thermal mass, which will slowly dissipate heat as the temperature drops.
They can be built (at home) from aluminum/wood/steel/whatever frames and panes of glass/plexi. If kept clean, you still get the greenhouse effect, with bleed-through of light, so they don't even cast a huge shadow over everything they tower around.
The turbines can go at the top, in the case of a large one, or several small ones around the bottom, where the cooler air is drawn in. In the case that the turbines are on the ground, around the perimeter, the friction in the turbines helps to heat the air as it passes over them, which adds a benefit of pre-heating the air as it's entering the chimney, and cooling the turbines, keeping them at a higher efficiency.