If you define fantasy as “a story that cannot occur in the real world”, as this web site does, then you can include sci-fi in that, as sci-fi takes places in worlds unseen and with technology uninvented, and any technology sufficiently advanced functions more or less like magic in the minds of many people.
But I’m not quite sure about that.
There’s definitely a link between sci-fi and fantasy, as both tend to be adventure stories. But Fantasy is by definition “unreal”, while sci-fi is “could be real”. Technology can seem magical, but it isn’t magic.
Which is why people tend to say “Sci-Fi and Fantasy” rather than just “Fantasy”. Related, but not a subset of. Because you can mix them, and the result is known as “Space Opera”.
Or is it? Here’s Tor.com working themselves into a later on the virtues of Space Opera, but holding off on really defining it (or refuting the statement that it’s Fantasy in Space). They talk about color and style, and poetry, but that seems to me a question of style, which is not really ontological.
To me, Space Opera means that there are elements of the universe that rely on speculative technology, space travel, and other Future Tropes, and also elements of the magical and supernatural. Star Wars is the most commonly known expression of this, but I think Dune qualifies even more, because with Dune the mystical/supernatural stands apart, plot-wise, from the tech. The Bene Gesserit and the Bene Tleilaxu are the institutional expressions of the cleavage.
What’s operatic in Dune is the struggle of Paul to understand himself, as well as the struggle against the Emperor and the Harkonnens. The remainder of the novels deal with the consequences of that struggle through the generations, as the metaphysical singularity represented by Paul is worked through by his son, Leto II, the God-Emperor.
The spice is real, and has a life-cycle, but it’s no less magic for all of that. It enables a mind to fold space and time, to see without seeing. The Worm is God.
If you keep the spice and lose the space travel, you have a struggle amid houses for dominance of the magic thing, which will play out much like A Song of Ice and Fire. If you keep the space travel, and lose the Spice, you have a sci-fi story about assassins and feudal regimes, with human enemies instead of aliens. The elements of each make make the other greater, while remaining distinct.