grammar - Are "Among …, include(s) ….” constructs illogical?

This website implies that "Among …, include(s) ….” constructs are untenable. It says that the sentence:

“Among the skills tested on the standardized tests given to military pilots includes orthographic imagination”

is illogical, because it uses both "Among" and "includes" when only one of these may be used at a time. The website also says it is acceptable to say “Among the skills is X,” or to say “The skills include X,” but not “Among the skills include X. ”

I don’t understand this, because in other websites I could see “Among ….. , include(s) …." For example, from here:

The University of Louisville’s online program consists of 36 credit hours, with 6 credits transferrable. Among the core courses include Philosophy of Higher Education, The American College and University, and Educational Resource Management in Postsecondary Education.

Incidentally, if "Among …, include(s) ….” constructs are acceptable, what is the subject of the verb include?