"Call a built-in" is a worthless kata idea.

Random test cases needed.

addWord(array, string){
array.push(string)
array=this.array
}
gives
Test Passed: Value == ["hello"]
TypeError: Cannot call method 'push' of undefined
at addWord

Tests are not testing the rights things in the right time and mislead to wrong assumption.

It is not clarrified that function must return the modified list. It is not clarified that the function should modify the list given as parameter.

It could be interesting to have a quick discussion on parameters passed by reference and by value in JS.

It could be more natural to add a function to the array prototype instead of creating a function.

Point out it should return the list

You should use a proper value for list in the example:

var list =  []
addWord(list, "hello") // list is now ["hello"]
addWord(list, "world") // list is now ["hello","world"]