I would define a classic as a game that is indefinitely re-playable. For single player gaming, this depends on that there will always be a way to compete with oneself.
In racing games one can compete with past lap records. In some strategy games it's possible to customise settings to make the game as difficult as one would wish. Such as playing against multiple AI enemies, all set to maximum difficulty level. These days, there might also be a mod to make the game more difficult. RPGs used to have limited re-playbability, given that there was a limited number of ways to play the vanilla game, and once you've tried them all at the highest difficulty level, it became less interesting to play it one more time. But for as long as an RPG has an active modding community, there will always be more quests to play through.
But one factor that wasn't really covered in the video, and which is difficult to analyse, is what is it about a game that makes one want to replay it? The narrator started off claiming that a game can be re-playable without being a good game. I see that as a false distinction. Can a game be good and yet not re-playable? Yes. But can a game be re-playable and yet not good? No.
In a racing game one can always improve how accurately one cut corners, and unless the physics is very simplistic, no one can probably do it to perfection. This means that if someone enjoys playing the game to begin with, that can serve as a motivation for replaying it. But if the game wasn't enjoyable, then it doesn't really matter that there will always be a way to improve past lap records.
I think that in order for a game to be endlessly re-playable, it has to appeal to us on a deeper level, in ways that may be hard to depict. That chess is still played today means there is something about the symbolism in chess that strikes a chord in us.
Nascar racing 2003 is perhaps the most popular nascar racing game in existence, still with an active modding community. Some state that it's because it captures the true feeling of Nascar racing, whatever that means. This, itself, implies that the appeal of Nascar racing isn't just a matter of watching a bunch of cars racing for x number or rounds until one crosses the finish line first.
How? You mean if you like a game, you re-play it regardless of its quality and replay value (replayability)?
For me, my taste matters. I re-play a game dozens of time if I like it. Plus since I'm old school, I don't get tired of playing retro-like games.
Sorry that I haven't answered yet. Indeed, I read your question earlier, but when I had tried to answer you I cried. Old good memories were visiting me.
Anyway, each game is something special for me. It's not like, you know, re-playable like trying to beat new score or speedrun it, but something beyond it. Yes, few games I was trying to beat just for score, it were: RE4 - knife&handgun only, RE: Outbreak and 2&3 - also with knife only. Manhunt 1&2 - to get higher score; Super Mario (NES) - to get new time limits, Super contra - to beat the game with several circles.
But most of the games like Mafia: City of Lost Heaven or Obscure series, or Penumbra, etc I play for expression, feelings, memories - everything that allows me to taste the game, to feel it. For instance, for some games I try to get some vine, and during the game I drink it slowly. Magnificent feeling. Such a "ritual" exists not only for games, but for watching movies. Eating potato chips isn't good for such epic western as "Good, Bad, and Ugly" or "Titanic".
As you see for me a game that is "re-playable" means plenty things.