Columnstore index query performance based on number of columns in SELECT statement
So I want to know, does number of columns affect performance of a
  query for a partitioned table with clustered columnstore index?
  If yes, then is there any way to measure performance difference?


Yes, the number of columns is often a significant factor for columnstore query performance as shown in shown in the last line your STATISTICS IO output. This is because columnstore allows data for only the columns needed by the query to be scanned. The elapsed time difference (247ms versus 52ms) indicates query performance is proportional to the number of columns (as I would expect), with elapsed time being the primary measure of performance. 

Although one can generally use elapsed time as the primary performance indicator, there are other factors to consider. Cached data or other activity on shared resources could affect timings.  Both plans are serial in this case so elapsed times are comparable for relative performance, with the assumption of a repeatable test in an isolated environment. However, if one plan were serial and the other parallel, the parallel plan could consume more CPU time than the wall clock time and result in a biased or incorrect conclusion (e.g. the query with more columns runs faster).