WalkSpeed value isn't changing?

Since you want to affect all players, you'll need to use a Remote Event, meaning you need BOTH a LocalScript and a ServerScript

I'm not sure what the function "ChangeText" is, but otherwise, your code should be structured like so:

Local Script

local frame = script.Parent
local remote = game.ReplicatedStorage.RemoteEvent

frame.TextButton2.Activated:Connect(function()
	frame.Visible = false
	for i = 3, 0, -1 do
		ChangeText("Start constantly running "..i, "Msgs")
		wait(1)
	end
	remote:FireServer()
	frame.Visible = true
end)

Server Script

local remote = game.ReplicatedStorage.RemoteEvent

remote.OnServerEvent:Connect(function(player)
	for _, v in pairs(game.Players:GetPlayers()) do
		local character = workspace:FindFirstChild(v.Name)
		if character.Humanoid.WalkSpeed > 16 and v.Settings.Playing.Value == true then
			v.Settings.Ran.Value = true
			character.Humanoid.Health = 0
		end
		wait()
	end
end)

You can also simply set the player's health to zero when you change the "Ran" Value instead of needing another if-then clause

If you simply want the individual player to die if their WalkSpeed becomes > 16 then you can use a while loop:

Local Script

local player = game.Players.LocalPlayer
local character = workspace:WaitForChild(player.Name)
local remote = game.ReplicatedStorage.RemoteEvent

while true do
	if player.Character.Humanoid.WalkSpeed > 16 then
		remote:FireServer()
	end
	wait()
end

Server Script

local remote = game.ReplicatedStorage.RemoteEvent

remote.OnServerEvent:Connect(function(player)
	local character = workspace:FindFirstChild(player.Name)
	if character.Humanoid.WalkSpeed > 16 and player.Settings.Playing.Value == true then
		player.Settings.Ran.Value = true
		character.Humanoid.Health = 0
	end
end)

Both examples have a RemoteEvent in ReplicatedStorage named "RemoteEvent" to make sure that the changes to the player happen on the server (where everyone can see them)