How to detect if someone is playing your game?

There really isn't a need to check that in a game because you can always check the person's profile, but I don't think it is possible to check across all servers and teleport to theirs.

• This was taken from here: https://developer.roblox.com/en-us/api-reference/function/TeleportService/GetPlayerPlaceInstanceAsync

local TeleportService = game:GetService("TeleportService")
local Players = game:GetService("Players")
 
Players.PlayerAdded:Connect(function(player)
	-- Is this player following anyone?
	local followId = player.FollowUserId
	-- If so, find out where they are
	if followId and followId ~= 0 then
		local success, errorMessage, placeId, jobId = pcall(function()
			return TeleportService:GetPlayerPlaceInstanceAsync(followId)
		end)
		if success then
			-- Teleport player
			TeleportService:TeleportToPlaceInstance(placeId, jobId, player)
		end
	else
		warn("Player " .. player.UserId .. " is not following another player!")
	end
end)

If you could somehow use a double for loop to check all the players of all the servers (something that would likely take time and resources depending on amount), to find the desired player then you could get the id of the server they are on and send the player there.