The statement claims that the attack was done in revenge for the deaths of Hamza al-Qu'ayti and his four colleagues in Tarim back in August 2008. Also of note, is the rationale for the attack: expelling the infidels from the Arabian Peninsula (see note on the previous post).
Update: There will be more on this later, but AQAP is quite explicit that it rejects the rationale that some have put forward that tourists and other non-Muslims that travel to Yemen are under the protection or guarantee of a Muslim government and are therefore not to be harmed. This, of course, is also one of the major problem with rehabilitation program and other similar program: if the individuals, or more usually detainees, don't recognize the state as a legitimate Islamic entity, then for many it matters little what the state approved scholars say, they are already guilty by association.
Update II: One of the things I neglected to mention last night - I was tired - was that despite the claim in the statement that the South Koreans were targeted because of their country's part in the War on Terror I think this is a bit of justification after the fact. I don't think the South Koreans were specifically targeted by the attacker, rather they were targeted because they were the biggest tourist group at the site where the bomber was waiting. If they had been Italians, Canadians, Spaniards or any other non-Muslims they would have been targeted. Their nationality, in this case, had little to do with the attack, and reporters and analysts who attempt to link the two are confusing issues that should be kept separate.