For example, if you knew exactly where Deep Blue would play on a chessboard, you'd be able to play chess at least as well as Deep Blue by making whatever moves you predicted Deep Blue would make\. So if you want to write an algorithm that plays superhuman chess, you necessarily sacrifice your own ability to \(without machine aid\) predict the algorithm's exact chess moves\.
Technically, couldn't we run by hand on a piece of paper all the computations that Deep Blue goes through, and this way "predict the algorithm's exact chess moves"? In a way intuitively I feel like it's wrong to say that Deep Blue is "better than" us at playing chess, or AlphaGo is "better than" us at playing go. I feel like it depends on how we define "better", or in general "intelligence" and/or "skill" – if it is related to a notion of efficiency vs to one of speed. Because in terms of pure "competency", it seems like whatever a computer can do, we can do it too, although much slower – by just executing each line one step at a time.
As far as I can tell, current AI systems can just explore the search space of possible moves faster than us. They aren't necessarily as efficient as us – arguably AI systems are still very sample-inefficient (i.e. AlphaGo trained on many more games than any human would be able to play in his lifetime).
Clearly though running through all the computations by hand would take an unfeasible amount of time. Not sure if this is just a minor philosophical point or an actual thing one should care about. I'm still learning more about the field, wouldn't be surprised if someone already talked about this difference between speed and efficiency in defining intelligence but I just haven't found it yet.
I guess what I'm trying to say is that I agree with the premise that "less intelligent agents will not be able to predict the exact moves made by more intelligent agents", but I'm somehow not convinced that DeepBlue or AlphaGo are "more intelligent" than us – depending on the definition of intelligence we use. And under definitions for which they are more intelligent than us, then I don't agree Vinge's Principle applies for them unless there are time constraints.
[The exact phrase that Deep Blue is "better than us at playing chess" – that prompted my comment – is actually mentioned in this page under the "Compatibility with Vingean uncertainty" paragraph]