I like to imagine game mechanics having a similar parallel to melody in music. While there are many factors in music, nobody every forgets a memorable melody line. I can still recall the entire Halo theme start to finish, despite having only briefly played the first one. I am sure there are still others who can never forget the Moon level theme in Ducktales. These songs, in a sense, are timeless due to their ability to stay with someone throughout time, always sticking in someone's head long enough to the point where people are searching on YouTube for the songs long after they have been made. Even though new music is made to accommodate new games, timeless music is never forgotten.
Likewise, I believe that game mechanics, very similar to melody lines, can become timeless. I always see people saying that they still play and adore SM64, despite being released nearly 20 years ago on far inferior hardware. A similar situation is seen with Chrono Trigger, and, having played it myself, I understand why. Good game mechanics, just like good melody lines, are never forgotten. They stay with a person throughout time, because that mechanic created a great deal of fun for that person, and having fun is what games are all about. FPS's today are constantly improving upon the mechanics set forth by Doom, which in a sense makes Doom a timeless game. Various ports and mods are still being made for Doom today, despite Doom being a very old game made in the days of DOS-BOX. The memory of Doom carries on in the spirit of FPS's. People may forget where game mechanics come from, but they will never forget what was enjoyable.
New games are made to improve upon the mechanics introduced in old games, just like how new music is made to improve their melodic structures. What it is that makes a good game good? And likewise, what makes good music good? By my definition, a good game has good mechanics, and good music has a good, memorable melody. Sure, old games eventually die out because of how old they are, but I never forget that game and how much fun I had with it. It's why I still have my N64, my SNES, my PS2, and my libraries of all three.