A:Answer Hello, Jay!
No, you do not need to have the Echo in order to use your Echo Show 8. The devices work independently of one another. The Echo does have a built in smart home hub which would help you to set up smart lights or other smart home devices that require a Zigbee smart home hub.
To connect your Ring doorbell to your Echo Show 8, you will need to open the Alexa app and enable the Ring Skill. Once you do this, you accounts will be linked and you can say, "Alexa, show me the front door" and you can view that camera feed from your Echo Show device.
I hope that information helped. Have a great day!