The wealth effect is commonly applied to two groups of people: those who perceive themselves to be richer and those who actually are richer. The slate article is really only trying to address the first group. Its questions whether feeling richer (due to assets like your house going up in price) really lead individuals to spend more money. For a piece that's supposed to "debunk" a myth, it does a horrible job. It doesn't provide any convincing data or give any detailed analysis. It jumps to the conclusion without any proof at all.
The article doesn't address the other group related to the wealth effect: Those who actually are richer. It doesn't try to touch that at all. Yet we're supposed to believe that the wealth effect has been officially debunked!?