Motorola's excellent track record with updating devices fell by the wayside as it became part of Lenovo and started releasing more device variants than anyone can keep track of each year. Nothing is better proof of that than the Moto G4 Play's situation. The device, which was released on September of 2016, has been stuck on Marshmallow 6.0.1 for months and months as owners gave up on even getting an update. Then the unlocked international variant started getting Android 7.1.1 last month and now the Verizon one is following suit.
Android 7.1.1 is rolling out in an OTA to the Verizon Moto G4 Play and it takes the device from build MPIS24.241-2.35-1-17 to NPI26.48-38. It ups the security patch level to December 2017, including the Krack patch, and also brings all of the Nougat goodies, including multi-window, bundled notifications and quick reply, granular notification settings, a customizable Quick Settings tray, and more.
The OTA size should be in the neighborhood of 1GB so make sure you're on a good connection and check for an update. If you don't see it yet, it might be rolling out slowly to users.