We'd be doomed anyway if a large enough asteroid headed towards us -- although the odds of that happening are fairly low, at least over short timescales. Even if this technique were shown to work in this small case, much larger asteroids would naturally require a much greater force to shift, and I'm not sure a rocket of this size would make nearly enough of a difference.
As to Rev. Green's question, I think the point is that, sure, you can use basic conservation of momentum to predict what would happen if the asteroid in question were a solid object. What I think they are testing is, instead, more the question, "does the asteroid stay in one piece after impact, or instead shatter/break down?" Or, in other words, are asteroids of this size even solid, in a meaningful sense?
I think they referenced "Armageddon" in the article, but annoyingly a better film with the same theme came out that year, in "Deep Impact", and there I think the missile-related approach failed because, rather than diverting the course, rockets either had minimal impact or merely split the giant rock into two slightly smaller, but still deadly, rocks. Granting that it's fiction, it's still an interesting and difficult question as to what happens when you try to blow things up. So it's good to test here, in a setting where thankfully our lives aren't at stake, to see how explosions or impacts affect asteroids in practice.