This exoplanet, one ”HD 189733b … resides a bit over 60 light years from Earth”. 60 light years. Thats 5.676×10^14 kilometres, or roughly 567 Trillion kilometres!
To figure out how fast the winds in the atmosphere are, you have to ‘look’ at the atmosphere. To do that, “…you have to wait for it to pass in front of its host star. Then, some tiny fraction of the star's light will pass through the atmosphere of the planet on its way to Earth.” And if it turns out that this light is ”… red- or blue-shifted due to the Doppler effect, then it implies the atmosphere is moving.” The extent of the red or blue shift, while factoring in the planet’s speed of revolution around its star, gives an idea about wind speed.
Think about the precision of the instruments used. This planet has an ESI of 0.88, so lets say its atmosphere is about as thick as Earth’s, approximately 100 kilometres. To figure out the red or blue shift of something a 100 kilometres across over a distance of 567 trillion kilometres is the equivalent of playing a video on your phone, placing it on Mercury and then watching the video from Earth.
It boggles the mind!