In your code, 0 is passed to Number.prototype.valueOf which just returns the primitive (0).
Which is essentially the same thing as
Number.prototype.valueOf.call(0)
If your code was:
let resultsArray = Array.apply(null, Array(10)).map(Number.prototype.valueOf,10);
The map() function would essentially be calling Number.prototype.valueOf like this:
Number.prototype.valueOf.call(10)
Here's the documentation - which provides a nice Polyfill that you can read and see exactly what map() is doing.
Strings would look like this:
Array.apply(null, Array(10)).map(String.prototype.valueOf,"10")
Which would output:
["10", "10", "10", "10", "10", "10", "10", "10", "10", "10"]
But surely you can do it in a more tricky way ;)
var resultsArray = '0'.repeat(10).split('').map(Number);
console.log(resultsArray);
And in case it's not necessary to get the numbers (but strings), it's even shorter:
var resultsArray = '0'.repeat(10).split('');
console.log(resultsArray);