Short answers, pulled from the story.
Tomonobu Itagaki created the Dead or Alive video game series while working for Tecmo in 1996. Itagaki developed the game to save his employer from financial struggle and established Team Ninja as a major industry force.
The Triangle System is a rock-paper-scissors mechanic where blows beat throws, throws beat holds, and holds beat blows. This system forces players to think three steps ahead and punishes simple mistakes instantly unlike other fighting games of the era.
DOATEC is the true antagonist of the Dead or Alive franchise and the organization that holds the World Combat Championship. The corporation conducts bio-weapon experiments and attempts to create the ultimate human weapon through the Omega Project.
The first Dead or Alive game introduced Danger Zones as interactive environments with simple explosive outer edges. Dead or Alive 2 evolved these stages into multi-tiered environments with falls and electrically charged walls.
The Dead or Alive franchise is controversial because it uses sex appeal to attract attention and has been accused of objectifying women. Critics have pointed to the Dead or Alive Xtreme Beach Volleyball spin-off as a particular point of contention for its use of female bodies.