The intrinsic electron-withdrawing nature of alkyl groups
I wonder if the pKa for water (15.7) is a typo. Usually we think it to be 14.0 (at 25C, anyway). And I wonder how much the gas phase acidity changes over this series.

Acidity in the gas phase means ROH must dissociate to RO- and H+ but doesn't put the proton onto anything else. Since the proton isn't solvated, it must have been knocked loose, say in a mass spectrometer, where the fragmentation potential can be measured. That just seems quite different from our usual idea of "acidity". But OK, it's an observation of a characteristic of a series of related compounds. 

The tendency to designate specific places for electrons (LUMO, HOMO) is understandable, but sometimes this description is uncertain and unnecessary. In a gas phase RO- ion, the negative charge is not 100% around the nucleus of the oxygen atom. Surely it will become unsymmetrical and drift where it might find a little positivity, like on the carbons and the hydrogens. Alkyl groups are polarizable and stabilize both anions and cations (https://onlinelibrary.wiley.com/doi/abs/10.1002/ejoc.200700004). 

It's simpler to explain the acidity changes in water and in the gas phase by referring to the size-dependent polarizability of the alkyl groups, but using molecular orbitals may have seemed better for publication.