The printing on the box is most likely the box manufacturer. The other box probably has it on one of the sides that's not visible in the picture. Most boxes even today include a similar marking, now standardized in a circular format. Non-test probably refers to the cardboard itself, the new boxes all include a "test" rating which is related to how much weight the cardboard can take without failing. I've never seen one labeled non-test, I think it is either really cheap cardboard or a company that didn't do the testing.
Some info here
http://www.masterpak-usa.com/masterpak.htm
I don't know exactly how the tests are done, but the info is probably findable with google.
The ones on Ebay have a glassmakers mark on the bottom that I believe is Libbey. Last company at the bottom of the page.
http://glassloversglassdatabase.com/marks/ats00003.html
Libbey was the glassmaker for a lot of novelty and commemorative glassware, including a lot of sports glasses and while the website doesn't push it they still do some similar stuff. Everything from fancy wine glasses to the mason jar with a handle sort of stuff.
They might have some info on who they made the glasses for. Maybe not, but it's worth a try.
https://retail.libbey.com/
Steve B