I am in no means an expert, but I'm willing to bet intercepting a non aerodynamic piece of rock that will reflect a radar signature as big as a house is a lot easier than a missile specifically designed to be aerodynamic and hard to hit. Entry velocities would be similar, video and article says this was a low trajectory entry, which if I'm not mistaken is the ideal ICBM trajectory as well.
You'd need a world wide radar network and a world wide missile network. Or at least one that covered all populated areas.
Even a smallish meteorite has a lot more mass than a missile warhead. You'd need something huge to shoot it down. Much bigger than anything available or envisioned
You wouldn't destroy it completely. Instead of one meteorite, you'd have a lot of smaller ones that would explode in the upper atmosphere, propagating the shock wave, and thus the damage, over a wider area.
These small to medium sized object aren't an existential threat to the human race. Sucks to be underneath one, but otherwise, life goes on as normal on earth. It would be cost-prohibitive to defend against them. The real threat comes from the large objects. Good news: We can pick them up well in advance. Bad news: We don't have any way of dealing with them should one be on a collision course. There are some ideas, but nothing on the drawing board yet.