And the nature of DoD research back then was more generally applicable to things besides killing. The Mansfield Amendment is what turned ARPA into DARPA and pushed to curtail pure research. If you couldn't kill someone with it, it wouldn't get funded.

    The Mansfield Amendment of 1973 expressly limited 
    appropriations for defense research (through ARPA/DARPA) 
    only to projects with direct military application. 
    Some[who?] contend that the amendment devastated American 
    science, since ARPA/DARPA was a major funding source for 
    basic science projects of the time; the National Science 
    Foundation never made up the difference as expected.

        https://en.wikipedia.org/wiki/DARPA#Later_history

The Internet didn't only come out of military research and spending. A lot of the technology, thinking, and origination came out of the private sector and universities as well. Not to mention the actual early days of the Internet were overwhelmingly private + university based, and not military. Nearly all of the advances that the Web was actually built upon, were not military. The deployment of Google occurred on top of an almost entirely private infrastructure circa the late 1990s. The specific technology stack that made Google possible at the time was almost entirely not military.