App is visible in My Watch list of apps but nothing happens when pressing on the INSTALL button.

The only other thing I can think of is to reset your Apple Watch and repair it to your iPhone and try again. Follow these steps below on how to do so.

Unpair and erase your Apple Watch - Apple Support

Set up your Apple Watch - Apple Support

Try restarting your apple watch. Follow these steps below.

1. Press and hold the side button until you see the Power Off slider.
2. Drag the Power Off slider.
3. After your watch turns off, press and hold the side button again until you see the Apple logo.

If your Apple Watch is charging, take it off the charger first. When your watch is charging, you can't restart it. 

Try this on your Apple Watch, go into the App Store and scroll all the way down to the bottom with your digital crown, and then click Account, then click Purchased, then click My purchases. If it doesn't show up their hit the back arrows and get out of that until your on the main page of the App Store and try searching for the app with the search button and see if you can download it from there.

What app is it your trying to install on your watch?

Your welcome, tell me if it fixes it and if you have any further questions about it.