What should happen when someone taps our app link on a laptop?

Send them to the web, not the store. A store link on a laptop is a dead end, so desktop taps should go to a responsive page or your mobile site that honours what the link promised, such as the same product or offer. Think of fallbacks as a ladder: the app opens on the routed screen; a phone user without the app goes through the store on a deferred deep link; desktops, unsupported regions and devices where the app is not available get a web fallback; and nobody lands on a store home page with nothing preserved. Newsletter readers mostly have the app already, so optimise for the direct open on phones and keep the web page for everyone else. Before each send, test installed, not installed, reinstalled, and unsupported region or device, and log which fallback fired. Fallbacks are set per link: https://linkrunner.io/deeplinks