Does "skew intake" mean "cherrypick (the students in admission)?"

covert selection practices are cherrypicking

the result of covert selection/cherrypicking is skewed intake

Skew is a mathematical term. Let say you are trying to find the average height of an American. You can't possibly measure every one of the 300,000,000 of us, so you want to find a small group to measure with the assumption that the average height of a small group of Americans will be the same as the average height of all Americans.

However, if the small group you choose is a professional basketball team, you will get the wrong answer. This is because the height of basketball players is skewed, i.e. because the height of a basketball player tends to be much different (higher) than the height of an average American.

So the implication here is that academy schools are using some secret process so that their students are different in some way than the typical student.

"Cherrypicking" simply means taking only the best individuals from a group.

Thank you both.
What does "intake" mean there? Admittance?

In this case yes. In general, intake means something you are taking in. If you were taking about diet, it might be food. If you were taking about car engines, it might be airflow. In this case it is students.

It may be an AmE v BrE issue but we usually refer to Admissions, not Admittance.