export default function move (array, moveIndex, toIndex) {
  /* #move - Moves an array item from one position in an array to another.

     Note: This is a pure function so a new array will be returned, instead
     of altering the array argument.

    Arguments:
    1. array     (String) : Array in which to move an item.         (required)
    2. moveIndex (Object) : The index of the item to move.          (required)
    3. toIndex   (Object) : The index to move item at moveIndex to. (required)
  */
  let item = array[moveIndex];
  let length = array.length;
  let diff = moveIndex - toIndex;

  if (diff > 0) {
    // move left
    return [
      ...array.slice(0, toIndex),
      item,
      ...array.slice(toIndex, moveIndex),
      ...array.slice(moveIndex + 1, length)
    ];
  } else if (diff < 0) {
    // move right
    return [
      ...array.slice(0, moveIndex),
      ...array.slice(moveIndex + 1, toIndex + 1),
      item,
      ...array.slice(toIndex + 1, length)
    ];
  }
  return array;
}

export default function move (array, moveIndex, toIndex) {
  /* #move - Moves an array item from one position in an array to another.

     Note: This is a pure function so a new array will be returned, instead
     of altering the array argument.

    Arguments:
    1. array     (String) : Array in which to move an item.         (required)
    2. moveIndex (Object) : The index of the item to move.          (required)
    3. toIndex   (Object) : The index to move item at moveIndex to. (required)
  */
  const item = array[moveIndex];
  const length = array.length;
  const diff = moveIndex - toIndex;

  if (diff > 0) {
    // move left
    return [
      ...array.slice(0, toIndex),
      item,
      ...array.slice(toIndex, moveIndex),
      ...array.slice(moveIndex + 1, length)
    ];
  } else if (diff < 0) {
    // move right
    const targetIndex = toIndex + 1;
    return [
      ...array.slice(0, moveIndex),
      ...array.slice(moveIndex + 1, targetIndex),
      item,
      ...array.slice(targetIndex, length)
    ];
  }
  return array;
}

Use of const and reduced duplication
Use of const and reduced duplication

Changed code to use const instead of let, as these variables should be read-only references to these values.
I've also removed the only duplicated variable definition; I've named it targetIndex as I couldn't think of anything better (naming things is hard!)

This is a great repo, perfect for implementing drag and drop state changes ;)