Multiplayer is less of a priority in games than it is today. Local multiplayer will continue to exist, of course.
Games will be more complete when they release, due to the lack of patches, and DLC won't exist. Physical copies will be just about the only way to play games.
Basically a lot of gaming will be how it used to be, but continue to evolve with better graphics and sound, etc.
There would still be expansion packs which PC had plenty of before online content, just no horse armor! Consoles would have gotten them as well with the addition of HDDs. Game stores would be thriving instead of dying. Many more games would have split screen multiplayer on consoles with lan play being a big thing as well. Lan parties would still be more prominent and gaming overall would be more social in the way that people would still be going over to each other's houses to play together.
Gaming would be more expensive though, no frequent digital sales, less competition from indies due to expensive distribution. No kickstarter, much less indie games or revivals of old games. No GoG, nostalgia gaming wouldn't be as big today. LBP, super mario maker, GT Sport would not exist. Minecraft might not have existed as well as many other games that were 'discovered' and crowd influenced over the internet. VR would have a lot less games, yet longer, higher quality games. Without the possibility to flood the market with cheap short downloadable games, only the best ideas would get published for the standard 60 or even 80 dollars per game.
Manuals would still exist, hint books, game magazines, tip lines, and people would actually play the game instead of watching you tube or follow a wiki on how to beat a game. Games would obviously be more focused on delivering the best single player experience instead of relying on online multiplayer. AI would be much better today, no multiplayer to provide the challenge. The focus on graphics would be much less, no internet, no minute comparisons between versions of games and consoles. No need for pro consoles and better focus on performance due to the lack of patches. Bullshots in magazines would of course still be rampant.
Overall I think gaming would have been more innovative than it is now. All the big cash cows rely on online multiplayer and DLC to keep people entertained for as long as possible. A games would still exist and not have been pushed out by mega AAA on one side and cheap downloadables on the other side.