Historically Southwest used "point-to-point" routes heavily. Basically the plane would go A->B->C->D over the course of a day. These would be fairly short hops, maybe an hour or two typically, and passengers going all the way to D would stay on the aircraft during each brief stop. I don't think they have any nonstop across the continental US; you must make one (or more) stops.
This may have changed somewhat since the AirTran merger, but I haven't flown recently.
the article specifically mentions 747s. 777s and 787s are regularly commuting trans-pacific these days; and have two- or three- tiered class seating; Presumably A340s and A380s, fit the bill as well.
I think long-haul flights more or less refer to flights that take longer than the ~11 hour flight crew shift.
Edit: apparently a long haul flight is any flight > 6h