Updating a 3rd-party app from the App Store?
How do I download an app to one of my devices through Apple's website when I'm not directly on that device?
iPhone 4s, iOS 9
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You can't, at least not directly.
If the device your want to download it on, has automatic downloads turned on in Settings->iTunes & App Stores, then anything you download on another device using the same Apple ID will be automatically downloaded to the other device.
See here: Update apps or use automatic downloads - Apple Support
Outside of that, there's no way to download onto a device remotely.