Why does this code work like this? What happened to the arrays as Value Types?

I think you might be confused about what a reference type is. The reverse method modifies the array it is called on, but that has nothing to do with whether the array is a value or reference type.

Take this code:

var arrayOfNumbers = [1, 2, 3]
var arrayOfNumbers2 = arrayOfNumbers
arrayOfNumbers.reverse()
print("Array 1: \(arrayOfNumbers)")
print("Array 2: \(arrayOfNumbers2)")

What do you think the printed output looks like? Well it looks like this:

Array 1: [3, 2, 1]
Array 2: [1, 2, 3]

The first array is reversed while the second is not. This makes sense as I only called the reverse method on the first array, but it only makes sense because an array is a value type. If it was a reference type then both of them would have been reversed because arrayOfNumbers and arrayOfNumbers2 would just be references to the exact same value in memory.

That is the main difference between value types and reference types. Value types retain their own copy of values while reference types just store a reference to a value. This is of course a bit simplified but should do as a basic explanation.