They look okay. They are mostly word problems which is better than 50 "find the derivative of" or "solve the following equation" type problems. But, it doesn't seem to be terribly focussed on proofs. It is more along the lines of "graph this", "determine that", "give a formula for...." Actually, Gelfand's Algebra is similar in that it is probably more non-proofs than proofs, but there are some good ones in there and the reason it is like that is simply because it has to bridge the gap between someone that cannot prove any theorems to eliciting that out of the student. In the later chapters, Gelfand is almost entirely dwelling (and I am talking about the exercises, here, not just the text) on the large project of actually proving inequalities between the arithmetic, geometric and harmonic means. There is a problem in the middle of the book to show that a polynomial of degree n is determined by n+1 of its values. He has as problems both to prove that the square root of two and to prove that the square root of three are irrational. (He provides a solution to the first and leaves the second unsolved for the student to do.) And, that's just "Algebra II" which is probably appropriately compared to the earlier parts of Exeter's problem sets.
Of course, the next question is whether or not you can get a 14 year old, say, to do all this. Maybe that is a lot more dubitible for Gelfand's book than it is for Exeter's program. I don't know given how selective Exeter is. But, then again, who knows what kind of students go through Gelfand's Correspondence Program and if they even do those problems at all? What I do know is that my oldest is 10 and he was jamming on the arithmetical problems in the beginning of Gelfand's book back when he was nine. He has been doing the Singapore series which we put him back into because we didn't want to take the chance that he was too young to sustain progress through Gelfand.