Your Problem

The parameter for your PlayerAdded event was playa, then you called the TableContains function using player.

player isn't defined! You have to call the TableContains function with playa.

But, you also called the TableContains function inside of itself, before closing the function with an end statement.

Fixed Code

local admins = {"ProjectRosploit","AlexTheOtaku","Lisforlucas","Ray5069"}

function tableContains(t, value)
    for _, v in pairs(t) do
        if v == value then 
            return true
        end
    end
    return false
end

game.Players.PlayerAdded:connect(function(playa)
    if playa and TableContains(admins, playa.Name) then

        --Your Code

    end
end)

Efficiency Edits

Make the table, a dictionary with players' names! That way you can index the table like admins[playa.Name] to see if the player is there, and you can eradicate the whole tableContains function completely.

Goulified Code

local admins = {
    ["ProjectRosploit"] = true,
    ["AlexTheOtaku"] = true,
    ["Lisforlucas"] = true,
    ["Ray5069"] = true
}

game.Players.PlayerAdded:connect(function(playa)
    if admins[playa.Name] then

        --Your Code

    end
end)

Your statement returns an error because player in player.Name is not defined. You probably meant playa.Name.

Also, format your code in an organized manner!

print'Player Kicker'
admins = {"ProjectRosploit","AlexTheOtaku","Lisforlucas","Ray5069"} 

game.Players.PlayerAdded:connect(function(playa)
    function tableContains(t, value)
        for _, v in pairs(t) do
            if v == value then 
                return true
            end
        end
        return false
        if playa and TableContains(admins, playa.Name) then

        end
    end
end)

The issue seems to be located in the function itself.

• The function is not called outside of its scope.

• The "if" is in the wrong place.

Let's make the function a static one.

print'Player Kicker'
admins = {"ProjectRosploit","AlexTheOtaku","Lisforlucas","Ray5069"}

function tableContains(t, value)
    for _, v in pairs(t) do
        if v == value then 
            return true
        end
    end
    return false
end

game.Players.PlayerAdded:connect(function(playa)
    if playa and TableContains(admins, playa.Name) then

    end
end)

Now we're getting somewhere!

Now, for your GUI, I assume it's already in game.StarterGui. So, let's define it.

print'Player Kicker'
admins = {"ProjectRosploit","AlexTheOtaku","Lisforlucas","Ray5069"}

function tableContains(t, value)
    for _, v in pairs(t) do
        if v == value then 
            return true
        end
    end
    return false
end

game.Players.PlayerAdded:connect(function(playa)
    if playa then
        local PlayerGui = playa:WaitForChild("PlayerGui")
        local Gui = PlayerGui:WaitForChild("ScreenGui") -- Or however you want to name it.
        local Frame = Gui:WaitForChild("Frame")
        if TableContains(admins, playa.Name) then
            Frame.Visible = false
        else
            Frame.Visible = true
        end
    end
end)

Since game.StarterGui replicates its children to the Player's PlayerGui, the GUIs will be visible to the people in the list. So let's wrap the "if" statement with a .CharacterAdded event.

print'Player Kicker'
admins = {"ProjectRosploit","AlexTheOtaku","Lisforlucas","Ray5069"}

function tableContains(t, value)
    for _, v in pairs(t) do
        if v == value then 
            return true
        end
    end
    return false
end

game.Players.PlayerAdded:connect(function(playa)
    playa.CharacterAdded:connect(function(Character)
    -- In this case, you don't need to see if the "playa" exists.
        local PlayerGui = playa:WaitForChild("PlayerGui")
        local Gui = PlayerGui:WaitForChild("ScreenGui") -- Or however you want to name it.
        local Frame = Gui:WaitForChild("Frame")
        if TableContains(admins, playa.Name) then
            Frame.Visible = false
        else
            Frame.Visible = true
        end
    end)
end)