The exact same thing happened to me with a Moto X (2013), though it's gradually gotten worse over the past few months. It started out as a purple flicker along the bottom of the screen, identical to what the linked video shows. It gradually creeped up to cover the entire bottom half of the screen during the flicker, and now the entire display flickers purple whenever Active Display kicks in (though the bottom half seems out of sync with its flicker). It also happens whenever I press the power button to turn the display on or off, though I'm not sure if that's also related to Active Display starting up and/or disabling.
Hard to say if this is a software issue or hardware (though it does worry me that it's getting worse over time). Waiting to see if there's any improvement once the Moto X 2013s are updated to Lollipop...