There are fewer connections between walking and meditation, although you can find new age relaxation remedies that try to combine the two. No matter, the practice of meandering has been connected with salutary effects for centuries. Medieval labyrinths were thought to provide pathways to commune with God, a kind of surrogate pilgrimage. Henry David Thoreau wandered the ponds of Walden in the mid 19th century at the same time as Charles Baudelaire wandered the streets of Paris, ennobling an increasingly alien environment with a kind of haphazard strolling, or flânerie.
The early PDP text adventure game Adventure (sometimes called Colossal Cave Adventure) was inspired by Will Crowther's hobby of caving. Later adventure games like Zork and The Legend of Zelda continued the lineage of exploration as a part of the experience, but the persistence of riddles, puzzles, and enemies quickly make calm meandering in these games difficult.
As so-called open world video games have become more popular, so larger and more complex simulated environments are available for meandering. Grand Theft Auto and games of its ilk retain some of the nuisances of gameplay -- police, rival gangs and so forth -- but their larger spaces also allow the player to hide from the game. One example is Jim Munroe's My Trip to Liberty City, a machinima travelogue of the Munroe's "walking tour" of GTA III's urban landscape.
The most meander-inducing of video game saunters must be Yu Suzuki's Shenmue. Although it is an adventure game by genre, a combination of abstruseness and free movement in the game's Yokosuka district makes wandering around this quiet city its own reward. Passing time and changing weather in Shenmue vary this environment, as do similar dynamics in GTA and Animal Crossing. In a game like Ico, not knowing whether a door is usable or not can lead to frustration. But in Shenmue, the slow plod up stairs to a row of apartments offers strange satisfaction.
Because relaxation and meditation rely on inaction rather than action, they threaten to undermine the very nature of video games. There is a fine line between producing Zen and satirizing it. The infamous, unreleased Penn & Teller's Smoke and Mirrors for Sega CD featured a minigame called Desert Bus, in which the player would make the eight hour drive from Tuscon to Las Vegas in real time, taking the wheel of a bus whose steering pulled slightly. Highway driving can indeed be calming, but Desert Bus is probably more conceptual art than meditation game.
As Animal Crossing invites, a real meditation game would reject graphical sensuality in favor of simplicity and austerity. I recently created Guru Meditation, a Zen meditation game for the Atari 2600 for play on a nearly forgotten 1982 Amiga peripheral called the Joyboard. The game also pays homage to an apocryphal story about how Amiga engineers tried to sit still on the joyboard's plastic platform to recover from frustrating kernel panics during the authoring of the Amiga OS.
My version is designed to be played by sitting cross-legged on the joyboard, without moving. Responding to flOw and Wild Divine's unfortunate conflation of tranquility and visual sensuousness, Guru Meditation takes advantage of the Atari's more primitive graphics to deemphasize a sensation of the outside world, in favor of an inner one.
As we think about Zen games on platforms more commercially viable than the Atari VCS, we may have to reject the ideology of engagement. Relaxation and reflection arise from constrained environments in which the senses are deemphasized and focused rather than escalated and expanded. Video games may often overwhelm and titillate our senses, but Zen comes instead from withdrawal and placidity. Video game Zen demands us to abandon the value of leaning forward and focus on how games can also allow players to achieve satisfaction by leaning back.