The general effect still exists, yes. It's just reported on poorly in this instance.
The 'relative overplacement' in the first table (the extent that participants over-estimated their own performance) is a correlation of 0.04, while the 'actual rank' is a correlation of 0.13, both in comparison to 'subjective social class'. There are a lot of correlations of higher magnitude than 0.04, so it's disappointing that the article attempts to focus on nothing else.
The 'relative overplacement' in the first table (the extent that participants over-estimated their own performance) is a correlation of 0.04, while the 'actual rank' is a correlation of 0.13, both in comparison to 'subjective social class'. There are a lot of correlations of higher magnitude than 0.04, so it's disappointing that the article attempts to focus on nothing else.