Choosing the rest of the players?

You can use table.remove when choosing alien so that it returns the removed value, while at the same time nullifying it from the table players.

Therefore, whenever you iterate through players later on in your code, it will returned everyone but the removed value, alien.

local playerstorage = game:GetService("Players")
local storage = game:GetService("ServerStorage")
local guifolder = storage.Guis
local players = {}

wait (40)
for _, player in pairs(game.Players:GetPlayers()) do
  if player and player.Character then
    local humanoid = player.Character:WaitForChild("Humanoid")
    if humanoid and humanoid.Health > 0 then
      table.insert(players, player)
    end
  end
end

if #players >= 2 then
  -- remove random value from table
  local alien = table.remove(players, math.random(#players)
  local alieng = guifolder.Alien
  local alieng2 = alieng:Clone()
  alieng2.Parent = alien.PlayerGui

  for _, player in pairs(players) do
    print(player)
    -- alien was removed, so this will return
    -- the list of all values inside of table `players`
    -- except alien.
  end
  --More code
else
  print '2 players needed!'
end

Also, in your first generic for loop, you are iterating through the table returned by players:GetPlayers, which only returns player objects.. therefore, you do not need to check if they have a character, because that's a given.

for _, player in pairs(game.Players:GetPlayers()) do
  local humanoid = player.Character:WaitForChild("Humanoid")
  if humanoid and humanoid.Health > 0 then
    table.insert(players, player)
  end
end