You don't need to array enter it because we are using SUMPRODUCT. Had we been using SUM then, yes, it would have needed committing with CSE.
How it works:
COUNTIF(Range,Criteria)
Countif is typically used to count a single criterion. We can however feed an array of values to the criteria argument, for example:
COUNTIF(Range,{"x";"y";"z"})
And in turn this will yield an array of results. For example {2;1;2} (e.g. suggesting two occurrences of "x", 1 of "y" and 2 of "z"). Typical of all array formula methods, Excel doesn't know what to do with the array result until we instruct it what to do with the array. To pass an instruction we have to choose a worksheet function. Here you want to know the combined count so you pass SUM or SUMPRODUCT. Hence:
=SUMPRODUCT(COUNTIF(Range,Array))