And, it's not only when it moves (or senses movement nearby) the display will "pulse" on and off periodically by design, more regularly if there are new notifications. If you swipe away the notifications it will not come on as regularly. It's actually one of my favorite features because of all of the different things you can do with it. Much more information than from a simple blinking LED.
If you're not familiar with how "Moto Display" works and all the things you can do with it, Google it! (there's a thread or two in this forum). It might just go from an annoyance to a nice feature!