I found a guide that says:

"Around 33% of the way into the game, you will receive a new sword. Continue on until you break a wall and the Prince says, ''It's said they built this palace on the ruins of another...'' Once you cross the next room, you will find a rotatable switch. Directly behind this switch is a breakable wall, although it doesn't appear to be one. If you hit it three times, you will find another room and you will receive a message informing you that Prince of Persia is now unlocked.
You can also rotate that switch until it points to the new room and it will open a gate that allows you to play Prince of Persia right there without having to exit back to the Extra Features screen."

I found the wall but cannot break it. Is this easter egg missing from GOG version?

The key combination mentioned in the video:

hold x, space, left mouse, e, c, e, space, left mouse, c

Is there a patch that restores Prince of Persia 1 and 2 from the Xbox version to the PC version? I want to play those versions of the game as well as the DOS ones, and my Xbox copy of Sands of Time only has the first game.