For "online" games (like this one), your picks are transmitted to the lottery office which stores them and then transmits the serial number back to the terminal

For "online" games (like this one), your picks are transmitted to the lottery office which stores them and then transmits the serial number back to the terminal, which prints the ticket. This prevents a ticket from being issued that the lottery's central computer doesn't know about. When it is time to verify the ticket, they simply send the serial number to the lottery central computer and that computer sends back the payout command (and invalidates that serial number from being paid by any other terminals.) The retailer is supposed to do some basic sanity checking for small prize amounts (is the ticket really on lottery paper, etc.) and obviously for larger prize amounts, there are several other methods to verify the authenticity of ticket stock that aren't public knowledge.