Can't download old app purchases through iTunes, only through iOS

I have been trying to download some old app purchases through iTunes, but I noticed none of the apps that are no longer available through the App Store show up.

These DO show up in the Purchases tab through iOS, though. But that doesn't help me, since my goal is to have a backup of these old games for when the App Store is not available (or remove these old stuff altogether in the future).

To clarify: I know about the Purchases tab. That's where I'm looking. I have checked if it's the same ID. I have checked if the computer is authorized. This only happens to apps that are no longer current on the App Store, all others appear fine.

Here's an example ('puss' in the Search tab):