Yes, you can import non-geo JSON files into QGIS but there are no native method for this in QGIS.
It's because in your link, it's non tabular data. For each "column" (like
income) per country, you have year and value. You need to preprocess the data to change the structure to flatten it to 2 dimensions.
One choice could be to use PyQGIS console to solve this issue. In first, you get the data with standard Python
json libraries and process it with Python. Then, using a memory provider, you can integrate the data as a layer and make your join. Be aware that if you need to reuse the data later, you will need to execute again the operations. So, you will need to save your memory layer or use the "Memory Layer Saver" plugin (but this plugin keeps data persistent per project).
Another choice could be to avoid QGIS completely at the beginning and generate a CSV from the data using Python (outside QGIS). Then, you can load the CSV file in QGIS.
For PyQGIS, look at the PYQGIS cookbook.