Push Notifications by default will open to the home screen of your app, this can vary based on how your app was configured. If you wish to change this behavior and redirect a PN to open a rich message It will require an app update to switch where push notifications drive in the app.
In order to have a Push Notification open directly to a Rich Message, you'll need to configure Rich Messaging for the campaign. This is found on Step 2 of creating/editing a campaign:
For more information on how to configure a Rich Message, please see the article here: Rich Messaging
Once the Rich Message has been configured for the campaign, a guest clicking the Push Notification should take them directly to the Inbox where they can view the Rich Message in its entirety. Please reach out to Punchh support by submitting a request here.