Not necessarily, because a pitcher doesn't always "gain ground." He must do so for it to be legal. If he does not gain ground, it's a balk. I had this occur last week in a D3 NCAA game. The pitcher did his jump turn, but his nonpivot foot (left foot, since he was a righty) just spun in its place as he turned toward first.

The NCAA has emphasized that its umpires watch this, as I guess they believe too many pitchers are, in fact, spinning and not really jumping and turning and gaining ground.

This is from the FED 2009 Rules by Topic book:

If there is a runner or runners, any of the following acts by a pitcher while he is touching the pitcher's plate is a balk (6-2-4)

Failing to step with the non-pivot foot directly toward a base (occupied or unoccupied) when throwing or feinting there in an attempt to put out, or drive back a runner; or throwing or feinting to any unoccupied base when it is not an attempt to put out or drive back a runner.

That's what makes your OP legal. F1 stepped (as part of the jump turn) to second when throwing there to put out or drive back a runner.