Information Age Does NOT Mean Modern or The Future
First, being in an Information Age does not necessitate being in the future. All it requires is for knowledge to be common and easy to access to everyone. It can be done with magic as easily as it is done with technology. Consider a world with vast libraries that replicate every book or note ever written via arcane works, and perusable from small crystals that are either in the pocket of every citizen or accessible from home. Yeah, that's an information age.
Accessibility Is The Key
To go further with the above point, I need to make it clear. The key to having an Information Age isn't whether or not there are vast stores of knowledge. The key is how accessible those stores are. For example, in many Sci Fi universes there are vast databases for every catalogued planet in a system, but the data is only accessible from certain ships and requires pulling navigation data from central locations.
The easier it is to update the information, access the information, and communicate with other people regardless of distance the more of an information age you are in. This is important to remember, because that makes these also the same levers you play with to keep technology super advanced without ending up in an information age.
Space And Distance
For Sci-Fi the fact that systems are light years apart is a big thing that can be used to slow down communication. Even with faster than light communication through quantum entanglement and super science, distance can make things harder to access.
For example, look at Star Wars. Star Wars has faster than light travel as a common tool, and faster than light communication. However, you can't casually communicate with someone in another system. To do t hat you need to access the Holonet, and only certain ships have access to the holonet. Without your own holonet access you need to go to a specific location to do research or communication, which is why Star Wars still has lore centers like libraries where people go to learn and research. Communication can be routed through holonet points to make personal communication, but this takes money and pull. Even then, it's less ideal than when you aren't having to forward a holonet terminal to a personal device. But now this is getting rambly.
The point is this: even with FTL travel, distances can slow down communication.
Security, Stand Alone Networks, And Post-Info Age Techniques
The other thing to remember is that advanced technology and security also means other ways of keeping data isolated. Even today we have security set up to protect information so it's not accessible to anyone who shouldn't access it. Cyberpunk is full of mega corps with stand alone networks that can't be accessed from off premises as a means of keeping data safe. As technology becomes more advanced, so to will be the ways to keep information from being accessed by those who aren't supposed to have access to it.
Going back to Star Wars, the Jedi Library was restricted to Jedi. To protect this you had to go to the Library in the temple on Coruscant. That meant visiting the temple, being surrounded in the center of Jedi power, and being in clear view of the librarians. Yes, you could access the data there, but you'd be seen, and certain sections of nformation weren't open to everyone.
The same can be done in other worlds. Data can be secured and not shared as a backlash of old problems. The new Battlestar Galactica did this a little with the breaking of networks to combat the Cylons, which in turn took the world out of an information age.
To sum this up, there are a few things you want to do if you want your game to not be in the information age with access to knowledge like how we have now.
- Information should require some effort to obtain, and not be casually accessed from on person devices or wherever out in the field without a link to someone in a place that can check.
- Communication over long distances (long is relative) should require effort or time to go through. Perhaps you have to have access to a specific non-portable thing, or go to a certain building.
- Remember: Communication is Information, treat them similarly.
Conversely, if you want to put a world into the information age, just reverse 1 and 2. Make information easy to access, and communication almost trivial. Whichever you want.