by SPBTooL
"You deal one extra damage when dealing damage."If you think of your neighbors as those with monsters in the same area as you, the only way you will get the extra damage applied is to first damage them with other card abilities. You can not attack monsters in the same area as your monster.
A monster in Tokyo that does two claws will send 2 damage to all monsters and the players to his left and right will take and extra damage each.
A monster out side of Tokyo that does two claws will do 2 damage to the king with +1 extra damage if that monster's player is sitting to the left or right if them. The player on the other side will not take any damage.
if you play a card that allows you to damage all monsters, the players to your left and right will each take +1 damage
The plural use of neighbor is to show that it is possible for more than one to be damaged. Not that both always receive damage.