A lot of older games had no save feature. Back in the days of the good old NES I think one of the zeldas had a battery in the cartridge for saving though.
The thing with those olds games, that, aside from some JRPG titles they didn't take that long to finish. I often played through games in one go. One of my favorites, Megaman 2, despite having a password system doesn't take more than 3 hours to beat. When I was heavily into gaming as kid, that was an amount I found reasonable I guess, since I beat it in single runs plenty of times, only upping the challenge by doing the bosses in a different order.
As for games that have no proper ending, I don't really worry over them either. If I beat the final level, I at least finished it. But with all these multiplayer games nowadays, there's no end to it. I mean, I haven't finished Team fortress 2, lol. As for sports games. Recently I bought Fifa 11 for about a buck. I've played through a regular soccer season, did a custom tournament, and by then I pretty saw all of Fifa again. Finishing first in a league to me feels "finished" in such games. Same goes for, for example, fighting games. Beat the final boss and you're done. Yes, I could replay with every other character and that's fine if one does, but it doesn't really change the fact that I already beat the boss.
There's a reason why I haven't listed Team fortress 1 or 2, as well as a few other multiplayer games on my backloggery account. It would just add to "unfinished" games despite there being no actual finish. Well, I guess... if you are world champion in any e-sport, I guess that's the "finish", but I doubt people will see this the same way universally.
