I understand that well, but I don't like it. Math for its own sake with no collection of reality alienates a huge category of people who might be interested in it if it was better explained.
The intended audience of AMS's Graduate Student Section is mathematics graduate students. Nevertheless, it's hard to say whether symplectic manifolds has any easily explained analogy for lay audiences. The subject originally arose from more abstract formulations of classical mechanics.
> a huge category
And I thought category theory was "math for its own sake"!