Push Notifications by default will open to the home screen of your app, this can vary based on how your app was configured.
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.