According to this person on Google forum, it is disallowing all Google:
Gold Product Expert Gold Product Expert
I think I found the root of your problem: http://www.rpgtherapy.com/robots.txt
Google can't crawl your website if you disallow all crawling.
Joy Hawkins, Google My Business Product Expert
Owner of Sterling Sky and the Local Search Forum"
I manually edited http://www.rpgresearch.com/norobots.txt through Plone site control panel, to allow all, and now it is starting to show up again, while the other sites are not. But I probably have the syntax all wrong. in the former, since I generally never touch the robots.txt
I see that the older server 4.3 (which works) has a much simpler robots.txt than the Plone 5 default (which isn't working correctly for Google): http://www2.rpgresearch.com/robots.txt
Is it the "Disallow /*?" line that is killing GoogleBot in the Plone 5 setup?