They call it flying because foils are flying through a medium, generating lift, just as the wings of airplanes do.
A big difference is that these wings lift the main body out of that medium (water) into a much less dense one (air), hugely decreasing resistance.
And yes, this doesn’t lift the boat completely out of the water, but airplanes do not get completely out of the medium they use (air), either.
Interesting point about not moving out of the medium. I don’t think this is terribly important but you could say that the airplane completely moves from the medium of wheels on the ground into the less dense medium of air.