Does something which affects "defending player" target that player?
No, it doesn't target. You are not immune.
If the word &quot;target&quot; isn't used, it doesn't target. Keep in mind that some keywords (e.g. &quot;Equip&quot;) use the word &quot;target&quot; in the abilities they represent, and the rules for casting an Aura use the word &quot;target&quot;.
You're asking about Annihilator, so let's look up what abilities it represents:

702.85a Annihilator is a triggered ability. “Annihilator N” means “Whenever this creature attacks, defending player sacrifices N permanents.”

As you can see, it doesn't use the word &quot;target&quot;. As such, it does not target.

In case you're interested, the following is the exhaustive list of what targets:

114.1a An instant or sorcery spell is targeted if its spell ability identifies something it will affect by using the phrase “target [something],” [...]
114.1b Aura spells are always targeted. [...]
114.1c An activated ability is targeted if it identifies something it will affect by using the phrase “target [something],” [...]
114.1d A triggered ability is targeted if it identifies something it will affect by using the phrase “target [something],” [...]
114.1e Some keyword abilities, such as equip and provoke, represent targeted activated or triggered abilities. In those cases, the phrase “target [something]” appears in the rule for that keyword ability rather than in the ability itself. (The keyword’s reminder text will often contain the word “target.”) See rule 702, “Keyword Abilities.”