Code (Skript):

1. on damage:
2.     victim is a player:
3.         broadcast "%victim%, %attacker%"

(You can find it in the docs)

 

you need to use victim or attacker on damage event, not player, even the error say that.

 

So, if I understand you, you want to do the script like this:

Code (Skript):

1. on damage:
2.     victim is not a player:
3.         if attacker has permission "staff.gamemode":
4.             set gamemode of attacker to adventure
5.         else:
6.             stop

(Code is tested and working.)
So if you hit a mob/animal, and if you have the permission staff.gamemode your gamemode changes to adventure

--- Double Post Merged, Sep 23, 2018, Original Post Date: Sep 23, 2018 ---

Code (Skript):

1. on damage:
2.     victim is a player:
3.         if attacker has permission "staff.gamemode":
4.             set gamemode of attacker to adventure
5.         else:
6.             stop

this is your code but "player" replaced with attacker. When you hit a player (and you have the staff.gamemode permission) your gamemode changes to adventure.

 

Code (Skript):

1. on damage:
2.     victim is a player:
3.         if attacker has permission "staff.gamemode":
4.             set gamemode of attacker to adventure
5.         else:
6.             stop