"Play only during your turn" (Investigation Phase) exists on both Shortcut and Shortcut (2). But this Shortcut (2) plays to attach, not to move. It then provide Move that is usable in any phase. I think the ability to fast Move outside of Investigation Phase is quite rare. (e.g. Pathfinder / Eon Chart has "during your turn".)
So you may find some niche use in Mythos Phase that you can suddenly move to change its difficulty. (e.g. Go to where your friends are to get commits, attempting to get Fieldwork boost, changing shroud that affects the test, alter skill card's value like Inquiring Mind / "Not without a fight!", etc.) Or some creative use in Enemy Phase by using the fast window after Hunter enemy moves but before it attacks (e.g. Get the engage and drag the enemy where your Guardian is, so they can respond with Dodge / Heroic Rescue / "Get behind me!" / True Grit, etc.) There is one window in Upkeep before readying the cards so you can still Move late if it turns out no one used it yet back in Investigation Phase.