The binary tree example is fine for very small and completely balanced trees, but for anything else you're going to get a lot of undefined entries in the array. There's no need for this; the array elements can be data structures like:

   { 'data': data, 'left': null, 'right': null }

When you insert a new child, you can just push it onto the end of the array, find its parent by comparing the 'data' values, and set the parent's 'left' or 'right' to point to the child's index in the array. Update the child's 'left' or 'right' as needed if the child isn't a leaf.

He mentions that you can build a traditional binary tree out of objects, but he makes it sound a lot more complicated than it actually is. His implementation of a binary tree breaks down at a scale where it's probably simpler and nearly as fast to just use an associative array and linear traversal, and he still requires writing the insertion, removal, and traversal methods.