Alright, so here's my understanding of it.
This man had renounced the United States and was actively conspiring to commit attacks against it, no? There is ample evidence of this in the form of propaganda videos distributed by Al-Qaeda.
So we have established that fact, now since he conspired to commit crimes against the United States and renounced the country, does that constitute renouncing his citizenship? If so, then there's no further case.
Next, Yemeni special forces have tried to apprehend him on multiple occasions, but became involved in firefights with the people protecting him and he managed to escape. If they were acting under orders from the US consul (which we don't know) then does that count has him being served? If so, then there's no case.
Also, he was posted online in publicly identifiable places as being a wanted man in the USA. If it is posted online in a place clearly visible for a reasonable person to see, then he was served his summons and there is no case. By not responding to his service of summons, he is pleading guilty in court and thus branded a traitor.
Finally, if none of those above facts count, can the Constitution - as it is currently liberally interpreted - implicitly allow the killing?
"Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort. No Person shall be convicted of Treason unless on the Testimony of two Witnesses to the same overt Act, or on Confession in open Court.
The Congress shall have Power to declare the Punishment of Treason, but no Attainder of Treason shall work Corruption of Blood, or Forfeiture except during the Life of the Person attainted."
Going part by part, I think its clear that he committed an act of treason via "adhering to their Enemies" Next, a person can be convicted based on the "Testimony of two Witnesses to the same overt Act" which I believe the Supreme Court would allow the videos he has made count as, or the people who traced back the explosive packages to him. Finally, "Congress shall have Power to declare the Punishment of Treason." This is the tricky part. Obama was in charge of the drone strikes....so unless Congress (or key members of it) were informed, then this is the weakest link to the chain.
Again, I think all of the above plus his name on wanted lists serves as due process, which means that the person is notified that he is wanted in court. By being on the most wanted list, and by being aware of that fact, I believe his process was served.