A spell's description tells you whether the spell targets creatures, objects, or a point of origin for an area of effect
So once again, you are the target of the spell, and while another creature can be the target of its effect, that only means there are two targets in total. Either of these is grounds for War Caster to not be applicable in rules as written.
That is blatantly wrong. The spell's description is this (I'm omitting the second paragraph):
You brandish the weapon used in the spell’s casting and make a melee attack with it against one creature within 5 feet of you. On a hit, the target suffers the weapon attack’s normal effects and then becomes sheathed in booming energy until the start of your next turn. If the target willingly moves 5 feet or more before then, the target takes 1d8 thunder damage, and the spell ends.
You are not the target. It says right there that the target is the creature you attack. You (the caster) do not suffer those effects.
The spell also includes the "range/area" text which shows that it is a sphere with a 5ft radius, with "self" as the point of origin. Interpreting that does require reading the spellcasting rules, but it does not specify "self" as the target. (If the "range/area" text just specified "self" with no area of effect, it would be saying the spell targets the caster, which is a special shorthand also defined in the spellcasting rules. But that is not the case here.)
I am not trying to convince you. I am refuting you. I am posting the rules to answer the poster's question.
MUCH LATER EDIT: for, uh, posterity, the breakdown of the actual RAW that people get confused by:
It says "Other spells, such as the shield spell, affect only you. These spells have a range of self." ("all wizards wear hats.")
The very next sentence says "Spells that create cones or lines of effect that originate from you also have a range of self, indicating that the origin point of the spell’s effect must be you" ("all fighters wear hats with feathers.")
It never actually says, or even implies, "All spells with a range of self affect only you." ("all people in hats are wizards.")
In other words, there are two distinct meanings of "self" showing up in the range/area section: one (alone) that means it targets the caster, and the other (with an area designation) that means the point of origin must be the caster. The distinction between the two will be apparent from the spell's full description.
That is blatantly wrong. The spell's description is this (I'm omitting the second paragraph):
You brandish the weapon used in the spell’s casting and make a melee attack with it against one creature within 5 feet of you. On a hit, the target suffers the weapon attack’s normal effects and then becomes sheathed in booming energy until the start of your next turn. If the target willingly moves 5 feet or more before then, the target takes 1d8 thunder damage, and the spell ends.
You are not the target. It says right there that the target is the creature you attack. You (the caster) do not suffer those effects.
The spell also includes the "range/area" text which shows that it is a sphere with a 5ft radius, with "self" as the point of origin. Interpreting that does require reading the spellcasting rules, but it does not specify "self" as the target. (If the "range/area" text just specified "self" with no area of effect, it would be saying the spell targets the caster, which is a special shorthand also defined in the spellcasting rules. But that is not the case here.)
I am not trying to convince you. I am refuting you. I am posting the rules to answer the poster's question.
MUCH LATER EDIT: for, uh, posterity, the breakdown of the actual RAW that people get confused by:
The developper also discussed it in lenght in a video Sage Advice: Target Revisited https://m.youtube.com/watch?v=xUOaQ_XY7wE