nope, StarCraft factions (most likely) come from Warhammer40k. - the Zerg (and its hivemind) are a version of the Tyranids [1] - the Protoss are adapted from the Aeldari [2] - the Humans are, well, Humans. with the ghost units being adapted from Psykers [3] and Marines being adapted from the 40k Space Marines [4]

The rumour is that Blizzard wanted to make a Warhammer game, but Games Workshop - the owner of the Warhammer IP - pulled out of the deal, so Blizzard modified their game's universe a a bit and called it WarCraft and later took a similar approach with StarCraft.

[1] https://warhammer40k.fandom.com/wiki/Tyranids

[2] https://warhammer40k.fandom.com/wiki/Aeldari

[3] https://warhammer40k.fandom.com/wiki/Psyker

[4] https://warhammer40k.fandom.com/wiki/Space_Marines