What utter crap. This is pure word play, it is an association fallacy, which is a formal logical fallacy:
The association fallacy is a formal logical fallacy that asserts that properties of one thing must also be properties of another thing if both things belong to the same group. For example, a fallacious arguer may claim that “bears are animals, and bears are dangerous; therefore your dog, which is also an animal, must be dangerous.”
Here, you have a property of the digital root concerning the numbers 3, 6, and 9. At the same time, you associate the same numbers with your imaginary friend, making them have a common property (3, 6, and 9). Thus, you make the association that one is represented by the other, without any other evidence than your assertion. Merely wishing this to be true does not cut it. Thus, you have used a formal logical fallacy in your premises. The rest of your faery tale “proof” is therefore meaningless arithmetic wankery.