While it's possible to inject the dragon capsule anywhere and get it's orbit in line with the ISS, its much more economical to inject it really close to the ISS so they dont need to do as much work to finish the trip.

They need to launch when the orbital plane of the station is directly overhead. The earth rotates surprisingly quickly, so even a minute or two later the plane of Dragon's orbit would be far enough off from the plane of the station that a couple expensive inclination change maneuvers would be necessary to line them up again.

Yeah, but the window is short because you have to catch the orbital plane, not the ISS itself. Earth's rotation speed is the relevant number here for figuring out how fast that plane sweeps across the sky.