This concept is sometimes known as "rod from god". The rod would have to actively steer through the atmosphere no matter if the target is moving or not. (Essentially it needs to be a robotic glider.)
The way this works is an orbiting satellite (probably orbiting west to east) fires the projectile so that the projectile's orbit intersects the atmosphere. Once the projectile hits the atmosphere, it uses its aerodynamic surfaces to curve its motion (which starts out with a west to east orbit that is very similar to its satellite) downward, toward the target. Without aerodynamic surfaces to cause a sharp turn, the projectile would just careen horizontally through the atmosphere until it had lost most of its orbital velocity. You want to preserve as much of that orbital velocity as possible and change the direction to be aimed at your target.
If your target is moving, the projectile needs to track that movement. One really big hurdle for this particular projectile is that it's moving very quickly, and you want it to hit a very small target. How does the projectile know where that target is located? It is presumably radioed the coordinates of the target before it launches, but how does it keep track of target movements once it launches?
Optical tracking would require a very powerful telescope. If you want to see human sized targets, that requires adaptive optics and a telescope the size of the Hubble space telescope. Your telescope needs to be in the nose of a hypersonic missile, which is an extremely harsh environment for anything, let alone extremely precise optical sensors and transparent windows. Also, there is cloud cover to deal with, and your hypersonic passage through the atmosphere will produce some amount of incandescent plasma in front of your camera.
It probably makes more sense to guide the projectile externally, and just radio coordinate changes up to the projectile. The satellite could presumably do this, unless it's night time or the target is obscured by cloud cover or trees or buildings. Another problem is that the time it takes for the satellite to talk to the projectile gets longer and longer the closer the projectile gets to its target. The one way delay is more than a millisecond, which might be uncomfortably long.
I think the ideal situation would be for the projectile to get multiple streams of data, one stream from the satellite, one stream from its own internal gyroscopes and camera, and at least one more stream from a spotter within a few miles of the target who can actually see it.
That spotter could be a person aiming a device at the target, or it could be a flying our ground-based drone. Regardless the spotter would likely be shooting a low power laser at the target in order to determine its precise distance from the spotter. Subtracting that distance from the spotter's GPS coordinates derives coordinates for the target. The spotter's scope would continuously radio these coordinates up to the projectile so it could alter its course. The projectile would also have its camera attuned to the exact wavelength used by the spotting laser, and it would steer directly for it as soon as it was detectable. The laser would not be visible to human eyes because it would be infrared.
A really good spotter system would also have a camera watching the sky for the glare of the incoming projectile. It would measure the angle between the spotter and the projectile in order to give the projectile more precise information about its current location.
Hopefully you're getting the sense that this is all extremely difficult. While I think it's possible to do at our current technology levels, I haven't heard of anyone doing so. I don't think a 100% hit ratio is ever possible with something like this (at least until some new, unforeseen technological breakthroughs occur). When describing this system, you should emphasize the extreme difficulty of its task, and all of the complexity of the data processing that needs to happen for the projectile to hit its target.
You should also emphasize the extreme physical conditions involved. The G forces would be extreme. The tungsten aerodynamic surfaces would be glowing white hot. The camera window would need to be actively cooled to delay melting and maintain transparency.
Regarding how much damage you could cause with this kind of projectile, it all depends on the mass of the projectile and how much orbital velocity it is able to maintain during its passage through the atmosphere. The wikipedia article you linked to suggests a mach 10 terminal velocity and a kinetic energy roughly equal to the projectile's mass in dynamite. (i.e. a 10 ton projectile results in roughly the same degree of damage that would be produced by 10 tons of dynamite.) In general though, I think it's easy to say that the projectile would produce much more focused and directional damage, whereas the dynamite explosion would produce equal damage in every direction.
One other clever trick would be to have the projectile break into zillions of tiny pieces right before it impacts (unless your target is a bunker 100 feet underground). This would increase the size of the affected ground and keep the damage focused on the surface, rather than spread out under the soil.