Update WebView without using Google Play I have an Android 6 device, where I have full root access. On this device, we are using an app which basically uses a WebView to display a website. The app is installed as a privileged system app. It is working good, however the webview-version on the stock device has a few bugs and we would like to upgrade to a more recent version.

I could update system.android.webview via Google Play, but due to the number of devices that need to be udpated this is not a viable solution. 

So my question is: How can I update the system webview on android 6 without google playstore? I need a way to extract the updated app from one device and install it on another without Google Play. 

Ideally,  we want to install without internet access but over adb so that we could script it easily for reliable installation on a larger number of devices.

The method suggested here for Android 5.1 seems to not work anymore on Android 6.
If you don't mind factory resetting your phone, you can try to unlock your phone's bootloader, flash TWRP Recovery and then install Open GApps, which installs/reinstalls Google apps and can give you ones that you cannot get from Google play.
Disclaimer:- I am not responsible for what may happen to your device during this process.
It installs WebView with it (if selected) and can remove stock (AOSP) Apps (Your default WebView). If it does not work you can still flash SuperSU and uninstall the system app.
-Daniel ✓

Edit: Since you already have full root access, you can try to uninstall WebView and install a fresh one from the web. Just be sure to download one prior to uninstalling.