I find it all very confusing, but I think that it's clear that a segment only counts once. "You can only count each hop, skip, or jump one time: once you’ve checked it off your list you can’t count it again." Thus a DCA>LGA "skip" would count as a shuttle skip, but not a "hop" within the east.
Interesting that this is segment based, not round trips.
Also note that travel must be booked after 7/7.