I have never heard of humans.txt before, but my first guess is that it does not help SEO in any substanial way. That being said, the homepage you linked to does encourage the use of <link type="text/plain" rel="author" href="http://domain/humans.txt" />. It's a good general rule of thumb to use the rel=author tag to link to a website about the creator of the specific webpage. Google likes to see this be a Google+ profile (hint hint wink wink) because then they can extrapolate all sorts of extra information about the author of the page content, but links to the author's blog, twitter, linkedin, career portfolio, etc. all work too. This actually used to be much more important than it currently is since Google deprecated authorship within search results in 2014 (because not enough people were using Google+, the theory goes).
All that being said, as humans.txt becomes more popular, I can see Google using it as a supplemental hint for the descriptions in search result pages, which today tend to be combinations of page content, the meta description tag, and Google's own fumbling around.
It appears to be a marketing stunt by Google to get people to see their careers pages and hopefully attract intelligent qualified people to work for them. It seems to have worked to a limited degree if you have seen it all over the web.