99% of the time when you got "random questions" like this in a game it was an anti-piracy trait. The idea was that people might be able to copy your disc, but they would be unable to play the game unless they could answer your questions - which would require the manual to be used.
(Bearing in mind that photocopiers were uncommon at the time.)
In the case of Leisure Suit Larry the opening questions were actually designed as an age-test. The intention was that "children" wouldn't know the answers and would be unable to play the "risqué" game.
At the time the game was released, the internet might be available in a modem that would go at the blazing fast speeds of a thousand bits per second. And of course, tie up your phone line in the process. The WWW hadn't been invented yet, let alone search engines.
Having been a kid during the formative years of the Internet, I can tell you that the notion of "you can find everything on the internet" doesn't really start coming into play until the early 2000s. In the late 90s, having to do research generally meant schlepping yourself to the library and finding encyclopedias or other research materials. Or, if you were lucky, maybe you had something like Microsoft Encarta, an encyclopedia on a CD-ROM!
If you got the software from pirate BBS, you would meditate on its file list to check for presence of notes, hints, FAQs and release info files if that information was not attached. Newsgroups/echomail could have it posted, too, routinely, or as an answer to someone's question.
That was a bit later, though. In the age of physical disk swapping, you would ask friends, or prepare for an audience with That One Guy Who Has Everything And Knows Everything.
