By definition a 'phenotype' is the expressed traits of a genotype. As far as I know there is no known gene or set of genes which express the 'phenotype' of 'Educational Attainment'.
I looked at the paper and the author provides no methods to replicate his study. For example, there is no discussion as to the SNP markers he was tracking to associate the 'phenotype' of EA.
What the author is implying here is that there is a gene for 'educational attainment' that is becoming more common in the population in general due to selection pressure.
I'm sorry but this is total hogwash. Anyone that correlates educational attainment to genetics is following a 'chopstick' gene.
Imagine that you correlate the ability to use chopsticks to genetic markers. What you'll find is that people with black hair and brown eyes have a much greater ability to use chopsticks then people with blond hair and blue eyes. You could even produce some pretty convincing graphs about this. However, as we all know the usage of chopsticks is cultural not genetic. There is nothing to prevent blond haired, blue eye people from using chopsticks genetically.
In fact you can correlate any two things that have no relationship to each other and find a correlation. For instance, the sun coming up in the morning and traffic congestion. They correlate, but have no causal relationship. i.e the sun does not cause traffic.