Edit: Just reread your question, and it seems the below is unlikely to be the answer. Most likely the developer just does not support the mode you want on the views you want it. I recommend going to the developer’s website and asking directly. Perhaps the feature can be included in the next update.
Sounds like it is an iPhone app, without UI (User Interface) support for the iPad.
Apps can be
iPhone only
iPad only
iPad and iPhone
The iPad will run most iPhone only apps, as long as they don’t use features not supported on the iPad (like making phone calls over the cellular network). However, they will be limited to the iPhone’s UI, which is almost always portrait only.
iPad only apps only run on iPads; usually because they have no support for the smaller iPhone UI.
iPad and iPad apps have built in interfaces for both devices, and will use the one approprate to the device they are run on.
When you search the App Store, you can filter by iPad Only and iPhone Only. Make sure your app shows up under iPad Only. Also, when looking at the screen shots, make sure they show an iPad landscape interface.
I did a brief search in the App Store for GoPro Controller, and could not find an exact match; so I can’t say if or which of these issues might be the problem.