The Alex/Mii Brawler represents the Piglin, a humanoid pig enemy in Minecraft who often appear in groups, with the two smaller-than-normal fighters representing the baby Piglins.
The Gold Alex/Mii Brawler starting off with a Killing Edge references how the Piglins can be encountered while equipped with golden armor and weapons, including swords.
The Mii Brawler's Pig costume, with DLC, references the unused Pigmen mobs that were prototype versions of Piglins.
The stage and music track represent the Crimson Forest, a crimson cavernous forest-like biome in the Nether which feature Piglins as enemies.
The second battle condition references how Piglins spawn in groups and attack the player if they attack a Piglin.
Other trivia:
This spirit's Attack type and Weapon Attack ↑ ability reference the Golden Sword, one of the strongest swords in Minecraft the Piglins can attack with.