The thing that really jumps out at me, as I read through the 1st Edition DMG, is the focus on long term play. 3rd Edition, the only one I've played so far, assumes the game tops out at about two years of solid play. I don't think the books explicitly discuss it, but that's the advancement rate built into the XP tables. Sure, you can go into epic, but then the game gets really dang weird, and you need another book.
4e goes even further. You can not play your character past 30th level, because at 30th level you get the power of "You die, but it's awesome." Which is perfectly good if you have one group of players and their awesome adventures, with plot arcs and so on. Eventually, you'll need to have a satisfying conclusion.
1st edition is different. Right off the bat, Gygax tells us that "Limitations, checks, balances, and all the rest are placed into the system in order to assure that what is based thereon will be a superior campaign, a campaign which offers the most interesting play possibilities to the greatest number of participants for the longest period of time possible." How well the system, the maths and so on, supports this, I can't say, not having played it, but that's at least what it's designer assumes you'll want to do with it.
The other main section that got me thinking along these lines was "Territory Development by Player Characters." You don't play your characters to the maximum level (or the maximum interesting level) and then start a new campaign; eventually, your characters should settle down, clear some land, and maybe continue adventuring but also start dealing with managing a stronghold and political maneuvering and so on. Then, even if that player leaves the game, the DM still has their character and their stronghold and their contributions made to the world, and can continue to use them as background for future adventures.
None of this is particularly new--I wouldn't necessarily have noticed it if I hadn't already read about the sandbox-y, multi-character nature of those early games, and their assumed end game. But it does seem to stand out.