Does counter-rotating propellers on multi engine airplanes have critical engine?
The term "critical engine" can actually refer to two very different factors: 


P Factor 
Engine driven accessories, depending on the airplane and how it's configured.


A twin with counter-rotating propellers doesn't have a critical engine from a controlability perspective, but very often there are important engine driven accessories, like hydraulic pumps, vacuum pumps, generators, etc. that are only installed on one engine, and if you lose that engine, well it's more of a problem than the other one. 

So you may lose the left engine and it has no effect on control or performance compared to the right, but that engine has the only hydraulic pump, so now you have to do the engine-failure-on-a-missed-approach song and dance, all while hand pumping the gear up.  Gets pretty busy.  In such a situation I'd consider the left engine more critical than the right one even though it's not a stick-and-rudder problem.

I think that's what the examiner was looking for.