I think the author misunderstands chaotic systems. Despite the presence of the phase 'deterministic chaos'...
Chaos, in math, is a technical term. It means, as the author said, that small differences in the initial conditions result in major differences in the outcome.
Imagine a small cannon situated in the end zone (or goal) on a football field. You point the thing at a 10 degree angle (up from the ground), use half an ounce of powder, and fire 100 cannon balls. Most of them land in around the same spot, lets say the dead center of the field. It's a quality cannon and there's no wind. You could plot the position of all 100 landing sites and observe a sort of bell curve... The distribution of cannon balls on the field has a point of highest density in the center.
Now let's focus on just that one most recent shot. Rewind time itself so that every atom in the universe is back where it was, and take the shot again. If cannon ball firing is truly deterministic, and even if it is chaotic, the cannon ball will land in the EXACT same spot, roll in the same way, and come to rest with the same side facing up.
Rewind time again. This time, change something... increase the angle to 20 degrees from the ground. The cannon ball will land farther from you than it did before. Repeat, but with 30 degrees, and it will land farther still.
You can repeat this rewind/re-aim experiment many times and measure every result and plot them and perform rudimentary number crunching and arrive at a model of cannons, then you can use your model to PREDICT where the ball will fall if you set the angle to 15.7 degrees... Cannon fire isn't particularly chaotic.
Switch from the cannon to paper air planes. Throw an air plane, see where it lands, rewind time itself, adjust the angle of your arm, throw again, and you won't be particularly surprised to see that the relationship between arm-angle and landing site is not as simple as the relationship between cannon angle and landing site. The danged plane may well land behind you.
But let's explore that. If you don't change the angle at all, if you only rewind time and throw again, and if paper airplane throwing is deterministic, and even if it is chaotic, then the plane lands in the same spot it did the first time, right? The exact same spot.
What happens if you only change the angle of the throw by 0.001 degrees? 1x10e-10 degrees? There is some change of angle that is small enough so that the plane will still land near the original site.
For those small changes of angle, you might even be able to come up with a model, and accurately predict where the plane will land.
Creating a model for larger changes of angle will be work intensive! If you can rewind time, and if you're patient, it's merely labor. That is, assuming that paper airplane throwing is deterministic and chaotic.
Of course, the model you come up with wouldn't be useful outside of that moment. Stop rewinding time, and you'll have different initial conditions for every throw. Air moves, grass grows, arms become fatigued, the sun moves, etc.
...In conclusion, if the universe is deterministic, then the only thing that makes chaotic systems unpredictable is that we can't measure angles finely enough--we can't measure anything finely enough.
Stephen Wolfram argues an additional point: that even with perfect measurements, the maximum speed at which we could simulate truly complex systems will always be slower than the natural execution of those systems (a human, the weather, etc), so they are predictable in principle but unpredictable in practice.