Learn German: Er spielt sich arrogant auf, als hätte er das Auto selbst gekauft. - He arrogantly puts on airs as if he had bought the car himself.

This is a special rule for unreal comparisons. When you use als to mean "as if", the clause uses verb-first word order, meaning the conjugated verb (hätte) immediately follows als. If you used als ob instead, the verb would go to the very end: als ob er das Auto selbst gekauft hätte.

Why do we need the Konjunktiv II form hätte here instead of the regular past tense hatte?

The Konjunktiv II is required because this is an unreal, hypothetical comparison. He didn't actually buy the car himself, but he is acting as if he did. The Konjunktiv II clearly signals to the listener that the action is contrary to fact.

What verb is being used in the first part of the sentence with spielt sich ... auf?

This comes from the separable, reflexive verb sich aufspielen, which means to put on airs, show off, or act self-important. Because it is the main clause, the conjugated verb spielt is in position two, and the separable prefix auf is pushed to the end of the clause.

Does selbst mean "even" or "himself" here, and how can I tell?