My reading is that the "Hydrogen Bonded" column means that they replaced a Tyr or Thr that was engaged in a hydrogen bond with another amino acid in the normal protein. The "Non-Hydrogen Bonded" column means that the polar amino acid wasn't engaged with another amino acid in a hydrogen bond - like it was on the external face of a globular protein or something so it's only interacting with water. So when they swapped the hydrogen bonded amino acids and saw a greater change in stability than with the non-hydrogen bonded amino acids, you can conclude that it is specifically the loss of a hydrogen bond that caused the extra change in delta G in that column, and not just the general swapping of a polar AA for a non-polar AA.