Uh, no. Chicago Midway happens to fit very nicely inside 1 mi² = 2.56 km². Its main runways (5 of them) with feeder ramps collectively take up at best ½ the space, so a single runway itself is not 1 km² but more like .2-.3 km².

Midway is an airport for ants. 10/28 at SFO is 2 sq km, and there are two of them, and 1/19 are 1.5 sq km, and there are two of them. Then you also have OAK and SJC.

Point: a square kilometer to generate 1GW peak of electricity would be an obviously excellent trade off, well within the cost parameters that humans are willing to spend on far less useful endeavors like runways and parking lots.

Wikipedia says that 10/28 is 3.618 km. For the runway itself to be 2 km², it would have to be 0.552 km wide. A quick glance at an aerial map indicates that a width of 0.552 km gives approximately the width of both runways, relevant taxiways, and the surrounding ground. Wikipedia says that the runways are in fact .061 km wide, for a total per-runway size of .221 km².

I picked Midway because it's a very conveniently sized airport, being almost exactly 1 mi² in a square-shaped with obvious meter marks (due to surrounding grid system).

Ok you got me. Bad at math.

Except that 1GW/km^2 is the absolute upper limit. As dreadmorbius computed, reality gives ~1.5% of that.

As I noted: real-world conditions demand 100x as much space.