With one purchase, you can download the in-app to all your iOS devices (iPhone, iPad, iPod).
There is a "Restore purchases" button in the Store section of Settings in iReal Pro where you can download the In-apps that you purchased before. 
You just need to be logged in with the Apple ID that you used for the original purchase.
If you still have issues after restoring, try to reboot your device.
You can't transfer it to your Mac as it is a separate and different platform.
Note: We do not have access to Apple's billing so if you're not sure that your purchase went through, contact Apple or look it up in your purchase history: