I actually don't think so, but I'm still not sure. The best example would be the movie "Titanic". While the incident has been real in the past, a fictional love-story is told. Does this make it to the category "alternate history"?
If you just change the actions of a few minor characters in relation to the big picture, I don't think it would be alternate history. For me, alternate history is when some crucial event in history has been changed. Hitler doesn't come to power. Abraham Lincoln isn't assassinated. Some important gadget isn't invented. Otherwise, almost any piece of fiction that takes place on Earth before the current moment would be alternate history.
I don't believe so either. Alternate history is more in the vein of changing major historical events rather than speculating about what was going on with people during a larger event. For ex if the Allies had lost WWII. That would be alternate history.
Saving Private Ryan isn't alternate history even though it never happened. Alternate history is a label assigned when major events have been portrayed as not happening the way they 'should' have (Braveheart is terrible for historical accuracy, but that couldn't be called alternate history because at no point was the movie's plotline focused on the concept of a pivotal event in history not going as we are aware it did). There is usually a focal point, when the change occurs, and other changes radiate out from that. A love story during WWII is not alternate history, but Hitler destroying the British Expeditionary Force at Dunkirk would be.
That is what both jeepea and I said though. Alternate history can't start when you start your story and your story can't be called alternate history. Some major event that changes the flow of history would have to precede your timeline. If the Byzantines hadn't lost to the Turks or if Attila had lived to conquer the rest of the known world or if the US had joined the Axis instead of the Allies in WWII or something like that.
I'm being nitpicky, but you quoted Jeepea's whole post and said that was alternate history, including the minor characters (I think you only meant to address the quote after the minor characters bit, but still...being nitpicky ).
Phillip Roth's "The Plot Against America" is a prime example of alternative history. In it, Charles Lindbergh gets the Republican nomination in 1940 and defeats FDR.