Death of the Author is just the idea that a work should be analysed based on the text of the work itself and not what the author says after the fact, what the author thinks of the work, or how the author's background personally impacted their creative output.
For example, a 'death of the author' analysis of Sonic the Hedgehog for the Sega Genesis would be analyzing the game's themes as presented in the game itself, analyzing the binary code, analyzing the player experience, analyzing the characters, etc based on how they are presented in the game itself and not the context of Yuji Naka or Naoto Ohshima or their thoughts on them.