Players must avoid hazards including Glam Rock boots
Called Back to the Studio, the game features tributes to each of the last seven decades.
David Holley, commercial director at the studios, said: "We want to mark the anniversary with something fun and easy that everyone can access.
"With Abbey Road's fame extending across the globe, we felt that using the website and an e-mail campaign was the ideal way to reach our fans."
In the game, launched on the studios' website, the player is a new recording engineer who, during his first session at the studios, accidentally presses a series of buttons which opens a rift to a different galaxy.
Mission
All the band's instruments are then sucked through the rift and sent to different decades in Abbey Road's history.
It is the player's mission to travel back to each of the seven decades and retrieve the instruments before the recording session starts.
Zombie-like engineers and other "baddies" unique to each era, including punks, Elvis look-alikes and a pair of huge glam-rock boots, attempt to stop the player.
Although the studios will be forever linked with the recordings made by The Beatles, Abbey Road has seen many major stars over the years from Glenn Miller to the Manic Street Preachers.
The London Symphony Orchestra were the first in the studio 70 years ago, when they recorded Land of Hope and Glory.
Miller recorded at Abbey Road during World War Two, before pop acts, including Cliff Richard and Cilla Black, made their records in the 1960s.
Soundtracks
In the 70s Pink Floyd recorded Dark Side of the Moon at Abbey Road.
Recently the studios have worked on several major Hollywood movie soundtracks including Shrek, Harry Potter and Lord of the Rings.
As well as the soundtrack for the forthcoming Sega game Headhunter, bands including Gomez, Spiritualized and The Divine Comedy have made their albums at Abbey Road.