Apple TV device not playing iTunes purchased movies
Apple TV device WILL NOT play iTunes purchased movies. Computer and Apple TV device are both logged in and using the same iTunes/ Apple ID account.
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What is your model Apple TV? Identify your Apple TV model - Apple Support
For Home Sharing purchased iTunes Store content, the Apple ID will also have to match the account that was used for the purchase.
For Home Sharing, use the Computers app on Apple TV, not the Apple TV app.
For Home Sharing purchased iTunes Store content, there has to be an online connection for the authorization ping.
The downloaded content will have to match the capabilities of the computer and the Apple TV box. E.g. if you download content in HDR, then you can’t stream that through Apple TV (4th generation or earlier). Adjust your download settings to ensure compatibility.