That would be as difficult as providing such a definition for "cheating," "stealing," or "exploiting." But the inability to quantify the phenomenon doesn't mean that it doesn't exist, just that its dimension is qualitative.
"Cheating" and "stealing" are not difficult to define. For instance, stealing is the unauthorized taking or use of something that does not belong to you.
In contrast, "price gouging" seems to mean nothing more than charging a price that is higher than someone else wants to pay.