There's no “two body problem” here, the solar system is an n-body problem.
And the “three-body problem” is overblown in pop culture: even n-body problems are fairly predictable in the short-ish term, it's just that you cannot predict things over a long period because measurement imprecisions have a snowball effect, but it's not particularly unintuitive (I'd say it's more intuitive than the idea that we could predict things with perfect precision over billions of years).
Well, the article says that the effect of the impact was much larger than the scientists expected. That doesn't really give a lot of confidence in how good we are at predicting these things.
