It's been a while but IIRC it was unconstitutional because the president cannot unilaterally execute a U.S. citizen anywhere without due process except under certain conditions, none of which were met in this case. It wasn't a declared war ("War on Terror" was a PR slogan, not a congressional declaration of war). I think the fact it was targeted specifically at a named person and there were no exigent circumstances (like trying to free hostages or stopping an eminent attack) were also factors. But, based on the plain wording, this wasn't a close or subjective call. To be clear, while it was illegal and unconstitutional, I don't personally think killing this guy was morally unjustified. He was a shithead who spouted anti-American, pro-terrorist crap online. But he was basically a poseur in a cave in Yemen. He was never a material terror threat to the U.S. other than making online videos. He claimed allegiance with real terrorists but they never took him seriously because he was a fucking American and they'd be stupid not to assume he was a double-agent.

You're not alone in assuming dropping a missile on this guy must have been legally okay because of the surrounding circumstances. I mean, that can't just... happen, right? The U.S. had already droned lots of non-U.S. citizen enemy combatants. The guy was clearly a wannabe terrorist calling for jihad against the great Satan America. He was awful and unsympathetic in every possible way. He was in a country (Yemen I think) that was fighting a declared insurrection-ish war against the local jihad group that sort-of associated with the guy. And that country was a U.S. ally. But... none of those circumstances made killing him legal. Yemen didn't launch the missile. A U.S. soldier under direct presidential order did. Legally and constitutionally, what Obama did was no different than Trump ordering U.S. soldiers to execute a U.S. citizen on the White House lawn with no due process. Except I highly doubt U.S. soldiers would do that without the surrounding circumstances of being a known terrorist, in Yemen, droned like they'd legally done before to similar non-U.S. citizen terrorists. Unfortunately, all of those circumstances were legally and constitutionally irrelevant. And, of course, even Trump would never give such an order because he knows American's sensibilities would be shocked, and both parties in congress would be forced to protest en masse, hold hearings, etc. But Obama and congress knew, in those circumstances, in that era, in that middle eastern country, against that unsympathetic target, it would encounter minimal protest. But it's at times like that and under circumstances like those that Rubicons get crossed and dangerous precedents set.

Sadly, that political calculation was correct. Despite being forcefully protested by a few members of congress, our system failed to work because the "War on Terror" was started by the opposition party and Obama's own party chose not to hold their President accountable for partisan political reasons. The media similarly followed party lines with the democratic majority choosing not to make an issue of it and the opposition media not wanting to go against the "War on Terror" they still actively endorsed. Only a few media people went against their traditional alignment and called it the unconstitutional execution that it clearly was. The handful of politicians, media and pundits who stood up on this issue despite doing so alone, are worth noting for their integrity. Even though they knew it might be politically costly and wouldn't change anything, they chose to stand on the right side of history in one of those rare moments when all others failed.