Short answers, pulled from the story.
Naughty Dog holds the most wins of any developer with five from ten nominations. Among publishers, Sony Computer Entertainment and its successor Sony Interactive Entertainment have claimed 15 wins from 44 nominations, more than any other publisher in the award's history.
GoldenEye 007, developed by Rare and published by Nintendo, won the first award in 1998, when the category was called Outstanding Achievement in Software Engineering. Nintendo also published the second winner, The Legend of Zelda: Ocarina of Time, developed by Nintendo EAD.
The award split into separate Gameplay Engineering and Visual Engineering categories in 2000. Those two categories ran in parallel for fifteen years before merging back into a single Outstanding Technical Achievement award in 2015, with The Witcher 3: Wild Hunt as the first winner under the unified name.
Four games won both the Gameplay Engineering and Visual Engineering prizes in the same year: SSX, Prince of Persia: The Sands of Time, Half-Life 2, and Uncharted 2: Among Thieves. No other game in the award's history achieved that double in a single ceremony.
Sony Computer Entertainment and its successor Sony Interactive Entertainment have published 15 winners and 44 nominees, more than any other publisher. Sony-published games won the Visual Engineering prize four consecutive years from 2009 through 2012, with LittleBigPlanet, Uncharted 2: Among Thieves, Heavy Rain, and Uncharted 3: Drake's Deception.
Assassin's Creed and Call of Duty each hold eight nominations without a single win, tied with The Legend of Zelda for the most franchise nominations in the award's history. Activision, the publisher behind Call of Duty, has accumulated 14 total nominations and no wins, the most for any publisher without a prize.