The article itself1 defines what the authors mean by both proteinuria and refractory:
...progressive proteinuria, with [urine protein-to-creatinine] values ranging from 0.6 at initial evaluation to 5.16 at highest (reference interval, <0.2), despite medical intervention with increasing doses of benazepril HCl (0.5-1.02 mg/kg PO q12h) and control of systemic hypertension.
Proteinuria is normally quantified as a ratio of urinary protein to urinary creatinine to account for the wide fluctuations in urine concentration according to hydration status. Normally, in humans and (apparently) in dogs, there is little to no detectable protein in the urine. In certain disease conditions (most commonly: hypertension and diabetes), proteinuria tends to increase with poorly controlled blood pressure/glycemia. Proteinuria2 may represent a novel risk factor for coronary disease in humans. Angiotensin converting enzyme inhibitors (ACEI, e.g. benazepril) and angiotensin receptor blockers (ARB, e.g. telmisartan) are commonly used to mitigate proteinuria (citing a dog article this time - this benefit is widely accepted in humans).
The point of this article seems to be that an ARB was superior to an ACEI to decrease proteinuria in this dog.
1. Sorry, I was able to access it through a library but free text is not available without such access to my knowledge. If it is, OP please post it!
2. Also sometimes measured (as in the cited article) as albuminuria - ratio of albumin to creatinine - rather than total protein. There are subtle differences is these approaches, but they are highly correlated.