How to restore individual app data from iCloud while keeping all the other apps installed and new data created since the last iCloud backup?
My own answer will be not applicable to every situation, but here is how I solved the problem.

All the data I needed from app in question (X) can be easily extracted once the app (with its data) is installed on the device.

So I did the following:


Backup the latest state to iTunes (saving a previous backup with "Archive" just before doing that)
Restore to the previous iCloud backup where the X app was still installed and had data
Extract all the data I need from X (I'm my situation, via iTunes > (my device) > Apps > Documents section
Restore back to the latest iTunes backup made in step 1
Re-install the X app in question from the scratch.