Did you read the complete article? I don't think so because it clearly stated what N1 and N2 are (IC3 = 7420 = dual 4 inputs NAND gates).
Since you see on the display which contestant has pressed first I don't see the interrest of a lamp for each contester. When they all are even fast all lights will go on with some ms delay.
But, if you still want a light I suggest you connect it after IC2 so that they will lit longer than the time the button is pressed. Of corse you will need some electronics (transistors maybe) to drive the lamps and also to reset them with S5. So a lot more for some useless lights (in mine opinion).
Let resume some things:
1) Read the complete article to understand it
2) All standard electronics from the shop on the corner
3) Forget about the lights
4) Still a problem? ask
Good luck