A Caesar Cipher is where you take each letter of the message, and count some number of letters further down the alphabet. For example, A becomes B, B becomes C, Z becomes A. The word DOG becomes EPH, if shifting by 1 letter. As can be seen, this forms a simple mapping from one alphabet to another. AES also maps from one alphabet to another. Except with AES, the alphabet is very large (2^128), and the way that it maps from one alphabet to the other is so complex that, without the key, no one can figure it out. Each key in AES creates a different mapping.
Wrapping back around to the method described in the OP, we can see that if you took the sum total of all the steps, what you're ultimately doing is mapping from one alphabet to another. Given a certain sequence of steps, we can map from a private key to a scrambled key. We have an alphabet of private keys, an alphabet of scrambled keys, and the sequence of steps describes the mapping between the two. As the OP mentioned, one can encode the sequence of steps as a list of words/numbers. This list of words/numbers describing the steps to take is the key (i.e. the password).
Therefore, this is not fundamentally different than AES or any other modern encryption scheme. As to whether the method should be used, I would strongly suggest no. This is because AES is well studied by the best minds mankind has to offer. We know with high confidence that it is secure. It is also specifically designed to resist all known crypt-analytic attacks. The method described in the OP is more akin to the Enigma Machine, which was completely demolished by early crypt-analytic attacks developed by people like Alan Turing.
If what you want is "security through obscurity", use the well studied methods for doing so. Stenography is a great example. Encrypt your data with world class encryption schemes like AES, and then use stenography to hide it somewhere. This is well studied as well, and if someone feels that obscurity adds an extra level of protection, that is the way to do it.