Is alternate history sci-fi?

I think it qualifies as SF. Ward Moore's novel Bring the Jubilee takes place in an alternate reality where the South won the American Civil War. Using time travel, the narrator goes back to the battle, changes history and ends up creating the world that we are familiar with. Another example is The Proteus Operation by James P. Hogan.

Obviously, not every alternate history story involves time travel, but Hugh Everett's "many worlds" interpretation of quantum mechanics puts alternate history on a science fiction footing. (In my humble opinion.)

Would you consider the man in the high castle sci-fi?

Yes, friends, governments in capitalist society are but committees of the rich to manage the affairs

"Would you consider the man in the high castle sci-fi?"

Yes. Most people would. It gets mentioned in all the science fiction encyclopedias. It's also part of the SF Masterworks series. Every "Hitler Wins" story is generally considered SF. I recently read another one called Swastika Night by Murray Constantine. It was actually written before World War II, so strictly speaking it might not fit the "alternate history" category. It still speculates on a nightmarish future, so, like 1984, it would be classed as dystopian:

https://www.amazon.co.uk/Swastika-Night-MASTERWORKS-Murray-Constantine-ebook/dp/B01DT7MWBA

I suppose you could consider alternate histories as examples of the many worlds theory of quantum mechanics, making them all sci fi.

But really, unless the story has some kind of science framework to make it so I wouldn't count it as sci-fi. So for instance S. M. Stirling's Nantucket series open with a freakish cloud of weirdness transporting the island back in time. That makes it sci fi to me. Ditto "Guns of the South", which has people producing an alternate history with time travel.

But if a book is just a "what if" story with no attempt to explain why the branching point happened differently, then I don't consider it sci fi.

http://www.sf-encyclopedia.com/entry/alternate_history

"It is a good thing for an uneducated man to read books of quotations" Winston Churchill (1874-1965)

My understanding is that sci-fi and alternate history are two sub-genres under the heading of "speculative fiction." Both types ask "what if?", but play out in different ways.

More on this: https://en.wikipedia.org/wiki/Speculative_fiction