Open my Apple subscription on someone else’s device?

To clarify further, taking advantage of Family Sharing is a developer's prerogative. Apple provides developers with the tools to implement FS into their apps. But it is up to the developer to implement it in their app, Apple doesn't make the decision that this app will allow FS and this app won't. So currently, someone at Atlantic doesn't understand how or doesn't understand the importance of coding FS into their app and no one has taken the decision to do so.

Before Family Sharing, to use your apps on someone else's device, you had to sign in to your Apple ID on their device and then designate that device as one of the devices allowed to use your content. According to your communication with Melissa, after you have installed your authorized copy of the Atlantic app on someone's device and authorized that device to use your content, you then need to sign in to your Atlantic account using your login credentials for the account, your email address & password.

For its own reasons, you've reported that the Atlantic doesn't allow multiple users for its subscriptions.

You are asking us to help you defeat that restriction!

M1 Mac mini, macOS 11.2.1; Watch, series 5 GPS/cellular, watchOS 7.3.1; iPad Pro 2nd Gen, iPadOS 14.4; iPad Air 2, iPadOS 14.4; iPhone 12 Pro, iOS 14.4; TV 4th Gen, tvOS 14.;  HomePods, audioOS 14.4 and Airport Express w/ Airplay 2