In some ways, the advent of so many new gTLDs may elevate the importance of the domain name itself.
1. People will relearn the value of typing in the domain name directly rather than sifting through search results. If a business advertises Chicago.hotels or New.app through non-internet media like television, radio, or print, wouldn't you expect people to try typing the new domain into the browser rather than searching for the words separately? This habit could be beneficial for direct type-in traffic across the board, including .com and other existing extensions. And it could, in a small way, circumvent search engines like Google.
2. Search engines, to stay relevant, will have to emphasize websites whose domain name corresponds to words that are searched for. Otherwise, if I am looking for Chicago.hotels by typing "Chicago hotels" into a search bar ... and I don't find the domain I'm looking for, then I will tend to rely less on search. As plenty of people have remarked, since Google has gone after so many new gTLDs, it is certain that the new gTLDs will rank well in Google. But how? Perhaps Google will tweak their algorithm to weight exact-match domains more highly. The component words in the domain name could become more important over the coming years, if search engines are to mirror the expectations of people who are searching for words on both sides of the dot.
Hard to predict. Definitely no more than 50% convinced by anything I say myself. But this does seem a possible scenario -- and a boon to quality domains of all kinds.