How is this 22 AWG cable rated 4 Amps?
Ampacity ratings for cables aren't hard numbers. Different insulation, different length, and obviously the environment all affect it. For example, the material information for that cable is pretty detailed and seems to use a polyurethane rather than your typical PVC.
I also do not think the 4A rating means 4A through every conductor at the same time. Probably just two.
14AWG wire for 5.5A is overkill though. An extension cord carrying designed to carry 15A is 14AWG. And on model airplanes, for example, they carry a lot more than 15A on 14AWG wire.