One word: Snake. The problem with games isn't so much technology as the industry's experience making them, with what really gets in the way of classics being usability issues. The simplest games, Pacman, Qix, Space Invaders, Tetris and so on don't put barriers in the way of your fun like, say, X-Com's hideous interface does. Something as simple as having to press Page-Up and Page-Down instead of using Mouselook, or an early adventure game being happy to let you get into an unwinnable situation, is just as important as how it pushes pixels around, and has little to do with tech (although of course, tech can enable better things). Case in point: Doom is still highly fun and playable. Heretic... not so much.

"Timeless classics" is also something of a misnomer. In most cases, they're introduced to people as that, so people think they have to enjoy/appreciate them. Look at the number of people who demand gaming's version of Citizen Kane, or quote Shakespeare or Dickens without actually having seen/read the originals.

(It's also worth noting that timeless classics are usually underappreciated in their day - often popular, but not necessarily heralded as a story for the ages. Dickens wrote chapter-based stories for newspapers. Shakespeare - to our knowledge - never thought anyone would want copies of his plays after their limited run and it's only through, bluntly, dumb luck that they survived. You need time to be properly timeless)

Really, what 'timeless' means is "has melted into the culture". Have games done that? A bit, but it's very early days. Pacman, Mario, Lara Croft and a few others have done it, at least for now. Remains to be seen how long it lasts, but still, gaming's early experiments are still being enjoyed today. Not something you can say for, say, Fred Ott's Sneeze over in film-land.