The 737 doesn't have any computers capable of assessing the aircraft energy state / flight path so the job is offloaded to the GPWS system. I imagine it was a convenient decision to hand the problem to Honeywell (or [insert manufacturer here]) than try to implement it themselves.
The FACs already have the job of continuously calculating energy state on the A320 series so adding a reactive windshear warning is trivial. I'm not convinced that windshear detection is based solely on AoA; instead the FAC is monitoring the total energy of the aircraft and if that drops below a predefined level than a reactive windshear warning is triggered.