They could have done a bit better with this quote ... we change the orbit of space-based objects all the time! So far, they've only been man-made space-based objects though. One thing the article leaves out is whether Bruce Willis will be on-board again.
An American, a Russian and the first Arab astronaut from the UAE all just headed into space together:
... I've always admired the capacity for various Space Agencies to put any current (geo)political, social etc. issues aside in the pursuit of science. This isn't a new thing, but you are right - we can all take a page from their book.
No mention about mass though, maybe because we don't know what the asteroid is made of?
I don't understand.
Change the orbit of another rock
for the first time in history.
How can changing an orbit of another rock be the first in history?
My english is not a native level.
I'm assuming "Another" refers to "A rock that is not earth." Though that does seem rather confusing.
1. We wouldn't be here if it weren't the case
2. They would have already collided.
Do we really want to destabilize an otherwise random asteroid's orbit unless it's certain it's on a collision course?
1. There are millions (billions?) of other asteroids that come close to us. What makes this one so special? Deflecting this one, even if the deflection works with no unintended consequences, does nothing to improve our odds against getting hit (P = P_one_asteroid * N_asteroids; N_asteroids - 1 ~ N_asteroids).
2. If the deflection destabilizes the orbit, where will the asteroid go but to a nice heafty attractor ?
The only value of this is if we're certain its on a collision course. But if we are, then it too late to deflect!
Second, your statement #2 is true, it caused a mass extinction event and probably paved the way for humanity to evolve. If we however get hit by an asteroid of that size again, chances are high that most of the population will die out.
There are not an infinite amount of asteroids, and in large time frames you can reduce their numbers. Therefore, we have a large hit once a century. Large, but largely inconsequential (The Earth is empty. Try this: Pick random coordinates and look them up on a map. Repeat. How long before you end up w/ 10 km of an inhabited area?)
Theories are infinite, funds are not. This is an ineffective solution (we can only deflect small and well predicted orbits) to an unlikely problem: mass extinction from asteroids hasn't happened in a very long time (millions of years) -> Bayesian inference -> very low probability of occurring soon. It will happen. But in a millions years
Compare that with the plethora of reasons we might die out in the next 10, 20, or 100 years.
Mass extinctions, from your number, appear to be a once in a 132 Mya event. 
Humans have been on Earth 0.1 Mya, 0.2Mya; statistically we'll be around for a total of 0.2 to 0.4 Mya in total. 
Therefore, there is a 1-330 chance of the two time lines overlapping.
 Assuming the present time is random, I believe the best estimate of event frequency is that we're in the middle of two occurrences; hence the doubling.
I'm being generous here. I don't think we have 0.2 Mya left in us, primarily because for the first time in history we have the ability to kill ourselves off. Therefore the assumption that out present in at a random position of the human experience used in  is invalid. Since we probably only have 100 years left, that's a 1-1E6 possibility facing us.
I think the theory is deflection of this object from its orbit could have all sorts of unintended consequence like a domino effect that cause either a chain reaction of events that lead this object or others on a collision course with Earth.
Sure, technically asteroids come in many sizes, but for dangerous ones you are talking about shooting a thing the size of a mountain that is falling towards you in a way that makes it stop falling towards you.
But jokes aside, I think the probability of altering the orbit to hit the earth practically non-existent, especially if you hit it when it is relatively close. You would want to hit it when it is the furthest away from earth to maximize your impact, so something > than 2AU or > than 300,000,000km.
I'm not sure if the formula to estimate the energy we receive from the waves is (Mass1+Mass2) * SomeConstant / distance^2 or it is Mass1 * Mass2 * SomeConstant / distance^2. I'm assuming that it is the first formula. If the second one is the correct one, you must add more "very" in my first paragraph.
« If it works, it will be the first time in history humans have physically changed the orbital trajectory of a space-based object. »
...because that happens every time we launch a rocket or land one.
The acceleration of objects in near earth orbit is vastly greater than the particles from a mine. Space ships collaring with super fast particles in the orbit could spell disaster for the spacecraft.
Hopefully we find ways to make the rock impact negligible if we ever get to the stage of unable to leave orbit due to collisions with space particles (Not saying subatomic particles I just mean debris)
Put another way, if you had 1,000 tons of mass to spread around earth orbit it would be difficult to effectively block rockets from leaving. Try to do the same thing with random orbits and it’s even less of a concern.