The bug preventing GTA 5 from being playable offline has been fixed
Yes, GTA Online does have a singleplayer campaign.

When the this was a bug, and they hadn't made any changes to GTA 5's DRM.
The bug has now been fixed, and there's a ticket for it on Rockstar's site. Here's the full text of it.
Question: Why can’t I set GTAV for PC to Offline Mode now that I have updated to the Rockstar Games Launcher?
Answer: In order to Play GTAV in Offline Mode, players will need to:
Run the Rockstar Games Launcher and update it to the latest version
Sign in to the Rockstar Games Launcher
Update GTAV to the latest version
Launch GTAV via the Rockstar Games Launcher while online
So there you go. You'll need to be online to launch it the first time, but after that you should be able to play in offline mode again.
The biggest gaming news, reviews and hardware deals
Keep up to date with the most important stories and the best deals, as picked by the PC Gamer team.

Jody's first computer was a Commodore 64, so he re having to use a code wheel to play Pool of Radiance. A former music journalist who interviewed everyone from Giorgio Moroder to Trent Reznor, Jody also co-hosted Australia's first radio show about videogames, how weird Lost Ark can get. Jody edited PC Gamer Indie from 2017 to 2018, and he eventually lived up to his promise to play every Warhammer videogame.