Verizon used to be a wasteland when it came to Android updates, but things are better these days. Sometimes it's even ahead of the curve. The Nougat update for the Moto Z play isn't exactly ahead of schedule, but today's rollout isn't bad for a non-flagship phone.
Hit the system update menu and you should have the option to download Nougat. You will need to be on WiFi to download the update, which has version number NDNS25.137-24-1-2. This is an update to the MCOS24 software build, so you'll need to be up to date in order to see the Nougat OTA.
The update includes all the usual Nougat goodies like split-screen apps, quick settings customization, and improved Doze Mode. This phone already has insane battery life. It's hard to fathom how amazing it'll be on Nougat. None of the Motorola-specific customizations appear to have been altered in this update.