(The key is that residues are created whenever a molecule of water is expelled. In theory, you can expel exactly one water molecule from each amino acid to create a residue, with one hydrogen from the amine group and the hydroxl from the carboxylic acid. In reality, it takes two amino acids to start the process of peptide synthesis, and each aa contributes only one part (either the proton or the hydroxl group) of the theoretically expelled water molecule. In reality its not even a single water molecule, as the hydroxyl group is going to pick up a spare proton from solution and the extra proton on the amine will get pick up by gawd knows what) <-- Downright wrong (at least, in regards to its importance to residues.).
The condensation is connected in this instance but not in all instances of residues. I think the usage is more clear if you look at some of the other examples in the biochemistry section of the wiki page "...a residue refers to a specific monomer within the polymeric chain of a polysaccharide, protein or nucleic acid. One might say, "This protein consists of 118 amino acid residues" or "The histidine residue is considered to be basic because it contains an imidazole ring." (https://en.wikipedia.org/wiki/Residue_(chemistry))