Thanks Greg! Leviton told me the same, that its GFCI does not have to use the grounding wire. I do not know why it does not trip/interrupt as the wiring is simple.

An electrician explained that because there is not enough current draining out the circurt without grounding conductor when "TESTing" to trip or interrupt when pushing the TEST button or using a GFCI handheld tester, it will provide protection needed in a situation of Ground Fault. Please advise. Thanks so much,
Hal