It applies to all white people. The white person you described, would be further disadvantaged in this Country if they were of another race (particularly black).
An African-American child, born of two African-American parents who are doctors, residing in an affluent suburb, with access to excellent schools, medical care, etc., certainly has advantages that a white child, living in a public housing project, in an impoverished area will not have. But the color of the African-American child's skin is not one of those advantages. And a white child with the same upbringing would have an advantage over the African-American child, even if it is a slight one. That is a privilege.