In order explain the inclusion of archae in the biological kingdom; it would be better to do a brief timeline of the taxonomic classification.
The taxonomic identifications for the biological kingdom before acknowledge five kingdoms (1969). They were the kingdoms Animalia, Plantae, Fungi, Protista and Monera. However, as the advancements in the classification of the genetic relationships of the organisms, the kingdom monera is further divided into two: the Eubacteria and the Archaebacteria (1977).
In 1990, biologist found it to be more convinient to use domains. Three domains were constructed: Domain Archaea, Bacteria and Eukarya. Domain Eukarya includes all the eukaryotes (protists, animals, fungi, and plants)
Today, Archaea is classified separately from Bacteria thus it stands alone as a separate kingdom. Though there are other researches showing different classifications.
The six kingdoms currently accepted are: Animalia, Plantae, Fungi, Protista, Archaea and Bacteria.