Minecraft – Kill skeleton horses with command block in a radius

Ok, so it turns out, my logic works fine, unfortunately sometime between 1.10 and 1.12 nested execute command support was removed. pity. If anyone has a different way of doing this, please let me know. In the mean time, I'm going to try and figure out how to do this without nested execute commands...

I am going to explain what your commands are actually doing.

execute @a ~ ~ ~ /testfor @e[name=damage-radius,r=5]

This means execute the command testfor @e[name=damage-radius,r=5] from the location of all players. This will result positive if there is an armor stand within 5 block radius of the player and run the next command. It does nothing to target the player. It only returns that there is an armor stand near a player.

/scoreboard players add @a damage-radius 1

This means add 1 to the damage-radius objective for all players. This does not target any specific player. This is your problem.

A better way to do it. First, skip the testfor. Second, run the command directly by targeting the player that is near the armor stand (Backwards of your method of targeting an armor stand that is near a player)

execute @e[name=damage-radius] ~ ~ ~ scoreboard players add @a[r=5] damage-radius 1

This means execute the command scoreboard players add @a[r=5] damage-radius 1 at the location of an entity named "damage-radius."

This will add 1 to the damage-radius objective of only the player that is near the armor stand.

Your other two commands will work as they are.