“Human is an animal capable of laughter” contains the same proximate genus as the complete essential definition. But the capacity for laughter is classified as a property, not the proximate differentia.
Comparison:
Hadd tamm: animal + rational (proximate differentia)
Rasm tamm: animal + capable of laughter (property)
A complete description can successfully identify the species; identifying it by a distinctive feature is not the same as explaining its intrinsic essence.