A 3 Game Guarantee Tournament simply means that every player is guaranteed to play a minimum of 3 games. 3 Game Guarantee Tournaments are set up similar to Double Elimination Tournaments. There is a winner's bracket and a loser's bracket, the main difference being players that lose their first two games will get to play an extra game in the loser's bracket in order to ensure everyone gets to play at least 3 games.

Example:
https://www.printyourbrackets.com/3-game-guarantee-tournament-brackets.html

A similar algorithm can be used to create 4 guarantee brackets, 5 game guarantee brackets, etc.