You're thinking about the speed wrong. At 1/4000th of a second, if it rotated nearly 4000 times per second, it would go all the way around in one frame. Talk about motion blur. :-)

It looks like the tip moved about three inches, so if we assume this fan is somewhere around four feet from center to tip (almost as large as they get), the circumference of the circle at the tip is about 300 inches. So it moved about 1/100th of a revolution in 1/4000th of a second. That should mean it spins at about 40 revolutions per second, or 2400 RPM.

That said, something is still off here. That's an entire zero higher than a real-world fan should ever spin, and then some.

According to UL code, the tip of an overhead fan can move at up to 3200 feet per minute, or 53 feet per second. At that speed, it should have moved 5/32nds of an inch in a single frame. This looks like it moved about three or four inches. To be fair, I realize that fans in India might not comply with UL rules for fan speed, but I kind of doubt they spin twenty times faster.

If you look at the metadata, I suspect that your camera overrode your settings. Many cameras have a feature called safety shift (or, I think the Nikon term is "Cybernetic override") that, in some modes, can change the settings from what you're expecting if the camera cannot achieve the provided setting in the available light. So if it could not shoot at 1/4000th because it couldn't crank the ISO up high enough and open the lens far enough, it might have shot somewhere more in the neighborhood of 1/200th (my best guess based on typical fan speeds).

Either that or that is one seriously fast fan.