And yeah, Steam itself is kind of a DRM.
This has no effect on games inside DOSBox, though. Just move the content to an independent DOSBox installation, and you are DRM-free and Steam-free. Works for any DOS game on Steam.
You must be online in order to play games. Even those that doesn't have anything to do with online service.
This isn't true. You need to be online to activate any game on Steam. You don't need to be online to play it. Unless, you want a multiplayer game over the internet obviously. Or some game comes with their own DRM and insist on it. Certainly not Doom or Quake and nothing from Valve itself either.