Let's take windmill like in the example, it has 3 blades, each maybe at most 5 degrees wide (out of the 360 for a circle). So that covers 15 total degrees or 1/24th the wind area, so at absolute best, it's about 4% of the wind power in that area being stopped. But the blades don't actually capture 100% of the wind power, a good amount will deflect off, those blades are not 5 degrees wide, they're less and they aren't straight blades, so again they capture less. Further the blade only captures a small vertical section of its own footprint, so it captures dramatically less wind power. Lastly blades are spaced with a good amount of clearance from each other leading to even less wind power captured. In aggregate, even by entirely layman measure, these likely have an immeasurable impact on another wind farm.

I'd bet if you built a mile high, mile wide wind capture device that captured 100% of wind power going to it, and then put a 2nd one 1 mile directly behind that, you could just maybe get a few % measurable impact.

It doesn't really even make scientific or math sense. Why? Due to why\how wind exists in the first place. You could completely block or "use up" 100% of the wind a windmill height, but it wouldn't effect anything at all for airspeed a km away. It's much the same way that you can have a leaf blower shooting out 300km\hour wind, but not feel it the slightest bit from 10 meters.

Air movement is constantly having to have energy fed into it in order to make it go anywhere. This is from uneven heating and air going from high pressure areas to low pressure areas. It isn't really made from the wind that's already moving around. If this weather guy wasn't actually just making a joke, he must be a terrible meteorologist for having such a poor understanding of something that should be directly in his wheelhouse.

it does make sense to me too. the effect is just not "big", whatever that means xD.