Peptide vaccines do work - there's a very similar vaccine currently in limited use (EpiVacCorona, running phase 3 trials in Russia, with emergency use approval granted in two countries at time of writing). The inhalation based delivery mechanism is also not novel, but almost never used because you need a whole lot more spaced doses than intramuscular, and that's a massive pain logistics-wise when you are trying to run a public vaccination campaign. There is no clear reason this wouldn't work. That said, there are many reasons it can fail in practice without a GMP environment - peptide chains are fragile and contamination is a risk - with a contaminated substance inhalation is going to be a much safer mechanism than injection, but unless repeated multiple times it will be less effective. The thermal disinfection stage needs precise temp control to not destroy the peptides and in general there's a lot of handling steps that can go wrong. But that's a matter of process, not of principle - both intranasal delivery and peptide vaccines have individually been shown to work.