Scripts not being able to change parents of objects?

This problem is quite common and a bit confusing at first, but it's quite easy to avoid once you learn how to solve it.

So what is happening is that you're setting a variable (in your case playerparent) to a property (in your case the parent) of an object, and when doing this the variable stores what the property was when the variable was set. So you're not storing a path to the property itself, but rather what it was when you set the variable.

This might sound a bit confusing so here's an example:

local part = workspace.Part -- A part

local anchored = part.Anchored -- You've now set the variable to what part.Anchored was (a true/false variable, also known as a boolean)

print(anchored) -- Let's say that the part isn't anchored, so it prints 'false'

anchored = true -- As we now know, anchored is a boolean (true/false) value, so we're actually just setting the value to true, rather than changing the property

print(anchored) -- Prints true, because we set the variable to true.

print(part.Anchored) -- Still prints false, since we set the variable and not the property.

Solving this is quite easy, since we're just storing a property of an object we can just reference the object itself and change the property that way. An example:

local part = workspace.Part -- A part

local anchored = part.Anchored -- You've now set the variable to what part.Anchored was (a true/false variable, also known as a boolean)

print(part.Anchored) -- Let's say that the part isn't anchored, so it prints 'false'

part.Anchored = true -- Now we're actually changing the property instead of the value

print(part.Anchored) -- prints true, since we anchored the part.

print(anchored) -- prints false, since we set the property to true but not the variable.

I hope those examples cleared a few things up, now here's your script but with the slight change:

while true do
	wait (0.5)
	value = game.ServerStorage.Map.Players
	timer = game.ServerStorage.Map.Time
	if game.ServerStorage.Map.Players.Value == 1 then
		for i = 20,0,-1 do
			if value.Value >= 1 then
				wait (1)
				timer.Value = i
			elseif value == 0 then
				timer.Value = 20
			end
		end      
		if game.ServerStorage.Map.Time.Value == 0 then
			print "LoadedMap"
			local themap = game.ServerStorage.Map.Build:Clone()
			themap.Parent = game.Workspace      
			tpposy = math.random(0,100000)
			tpposx = math.random(0,100000)
			tpposz = math.random(0,100000)
			themap.Part.Position = Vector3.new (tpposy,tpposx,tpposz)
			print (tpposx)
			wait (1)
			local players = game.Workspace.PlayersMap:GetChildren()
			for i = 1, #players do
				playerthing = players[i]
				rootpart = players[i].HumanoidRootPart
				playerparent = players[i].Parent
				wait (0.5)
				rootpart.CFrame = CFrame.new(tpposy,tpposx,tpposz)
				rootpart.CFrame = CFrame.new(tpposy,tpposx,tpposz)
				rootpart.CFrame = CFrame.new(tpposy,tpposx,tpposz)
				rootpart.CFrame = CFrame.new(tpposy,tpposx,tpposz)
				wait (1)
				player[i].Parent = game.Workspace -- Changed here
				print "Parent Changed"
				game.ServerStorage.Map.Players.Value = 0
				game.ServerStorage.Map.Closed.Value = true
				actualplayer = game.Players:GetPlayerFromCharacter(playerthing)
				playerweapons = actualplayer.Inventory:GetChildren()
				playerweapons.Parent = actualplayer.Backpack
			end
		end
	end
end