Neural networks are universal approximators. Choose a function and get enough data from it and you can approximate it very closely and maybe exactly. If initially creating function F required algorithm Y ("search" or whatever), you can do your approximation to F and then say "Look F without Y" and for all we know, the approximation might be doing things internally that are actually nearly identical to the initial F.
What is interesting is performing well under reasonable computational constraints i.e. doing it faster/with fewer flops than stockfish.
Also found in the paper: "While our largest model achieves very good performance, it does not completely close the gap to Stockfish 16". It's actually inferior but they still think it's an interesting exercise. But that's the thing, it's primarily an exercise like calculating pi to a billion decimal points or overclocking a gaming laptop.
So the network still needs to do some impressive generalization in order to „interpolate“ between those samples.
I think so, anyway (didn‘t read the paper but worked on alphazero-like algorithms for a few years)
But if someone grew an actual dragon in a lab by splicing together DNA fragments, that would still be a major feat. Similarly, training a neural net to play grandmaster level chess is simple in theory but extremely difficult in practice.
So you're estimating from data a function which is itself not necessarily optimal. Moreover, the point is more like how far can we get using a really generic transformer architecture that is not tuned to domain-specific details of our problem, which Stockfish is.