You can push your Ring’s physical button and check Hubitat device’ event history to see what value it reported in the pushed attribute, and use pushed as the attribute in the rule trigger with the value you found to trigger the rule when some pushes the Ring’s button.
Unfortunately, Ring doesn’t support RTSP and there is no official way to pull the live stream, so you won’t be able to display the video/image on the dashboard. But the you can have the Fully browser to open the Ring app automatically when someone pushes the button by using the following intent URL. The down side is Ring app doesn’t support redirecting to the specific camera’s view page with the intent URL, so you will have to tap the specific camera to view the video.
Ring intent:#Intent;launchFlags=0x10000000;component=com.ringapp/com.ring.launch.LaunchActivity;end
Rapid Ring
intent:#Intent;launchFlags=0x10000000;component=com.ring.answer/com.ring.answer.presentation.splash.SplashActivity;end
Or you can try another approach described by @Automated_House to use Alexa Routine to show the ring camera on the Fire tablet. You can create a virtual-contact-switch device using the HE community developed device handler, and turn this virtual device to on (open) in the rule, and have the Alexa routine to be triggered by this virtual device. (Alexa routine cannot be triggered by “switch”, but can be triggered by the contact open/close.)
I have other RTSP enabled cameras feeding the live streams to the dashboards via Blue Iris, so my rule was asking FKB to navigate to my “security” dashboard when someone pushes the Ring button.