>Has there been any good application of "periodic table" as a visualization method for anything other than chemical elements?
No, because as can be seen in all of them the structure of the table maps to the structure of the chemical elements.
The visualization of chemical elements is successful because it is an accurate representation of how chemical elements work, it does not just represent data but also is mapped to a model of how that data can conceivably change in the future.
Every periodic table of X that is not chemical elements is stupid and does not work because
1. come on - what are the odds that some other subject in the universe has a similar model to chemical elements.
2. the visualization is not done to best represent the data but the data is bent as best as it can be to fit into the periodic table structure.
And what is meant by periodic structure here - it is meant a selection of cells laid out in a very specific way with a color scheme so that if you saw it far enough away you would instantly think - hey, it's a periodic table!
The periodic table used this way is not a data visualization method, it is a visualization parody
method.
on edit: also pisses me off because in my world a parody should at least be funny, darn it.
sorry for the rant, this stuff really pisses me off.