Why does my GUI text not change to the intermission time?

First of all, your status variable needs to be the instance of the StringValue itself and not the value because you need to change the value later on. Second, you should add a wait() around line thirteen where the script is counting down the intermission. Third, your script needs a way to break out of the for loop just in case a player leaves while the game is counting down. Finally, the script should probably be able to break out of the while loop as well when the game starts. This would make the script look like this:

 --// Variables
local MapStorage = workspace.MapStorage
local IntermissionTime = 15
local Players = game.Players:GetChildren()
local Status = game.ReplicatedStorage.StatusValue
local RoundInProgress = false

--// Intermission
while wait(1) do
	if not RoundInProgress and #Players > 2 then
		local startRound = false
		for i = IntermissionTime, 0, -1 do
			if #Players < 2 then break end
			Status.Value = "Intermission: ".. i
			wait(1)
			if i == 0 then startRound = true end
		end
		if startRound then break end
	elseif not RoundInProgress and #Players < 2 then
		Status.Value = "2 or more players are required to start"
	end
end