True, but, I doubt that Doomhammer did recognise Ner'zhul's authority. Either way, the connection is only in the "office" (that word sounds really out of place there...) of warchief, nothing else.
I do not dispute that. I am just saying that they do not even have a king, there isn't any semblance of a dynastic reign, etc. While there were elective monarchies (Kingdom of Bohemia did elect kings when needed, for example) and there is something of the matter nowadays (the case of Andorra, though it's... really unconventional nowadays), they resemble the orcish nation even less.
I base my opinion on the facts that we do not know of any event where the Kingdom of Stormwind did enter the Alliance of Lordaeron - the Alliance of Lordaeron did restore Kingdom of Stormwind, but that doesn't imply membership either - NATO restored the Republic of Afghanistan (I believe the proper name is different, though), however, Afghanistan is not a member of the organisation, the fact that we do not know of any event that would signify that the institutions of the Alliance of Lordaeron would be moved to Stormwind (or elsewhere). Anduin Lothar was both a supreme commander of Alliance forces and the Regent of the Kingdom of Stormwind, however, that at best implies some sort of weird personal union. He did convince others to ally themselves against the orcs, however, he never did come under the command of either of them, which, yet again, doesn't imply membership. Varian Wrynn, who was the sovereign of Stormwind back then (as recognised by the kings of the Alliance kingdoms), is nowhere mentioned to have ever agree or have his kingdom enter membership of the Alliance. Lack of a treaty legally means that no relationship between two legal entities exists in the issue of said treaty, thus, if there is no known event/list that would state that Kingdom of Stormwind is a member of the Alliance of Lordaeron. The other kings are portrayed to agree on forming the Alliance, however, nobody from Stormwind is ever shown to do so, nor are they actually stated to be in that alliance before the fall of Lordaeron.
As for the Alliance of Lordaeron being called "Alliance of Lordaeron",
http://wowpedia.org/Alliance_of_Lordaeron - there you go. I am aware that "Azeroth" is listed there as one of the Seven Kingdoms, however, the book Tides of Darkness does nowhere state that Stormwind actually did enter the Alliance (while the other kings are shown to agree to their membership, one way or another), and since Warcraft II has been retconned more times than I can count, I do not consider it a reliable resource anymore (and instead go with the books and WoW ingame material). However, the article clearly states that Alliance of Lordaeron was a predecessor of the current Alliance, thus significantly implies that the Alliance of Lordaeron and the current one are two separate entities, membership notwithstanding.
That, and if Kingdom of Stormwind was also a member of the Alliance of Lordaeron, then we come to a rather BIG problem - it starts to give credibility to the Alliance claim to Lordaeron, and I probably do not have to state what that would imply.