Unique device identifier would be some information unique to your device that can identify it. A common example of such a unique Id would be your IMEI although that isn’t necessarily what they are using. Minecraft as an example creates a unique user ID based on your account that system administrators can use to keep your player records even after you change your Microsoft account name or gamer tag.

It doesn’t have to be specific data related to your activities in the app per se, but it could potentially be used in that manner depending on the app.