With windmill waltz flurry and the other Dance strikes, the step movement happens after the attack, so there's no targeting issues, and the other movement is part of the action of the strike and not linked to the attacks at all. Ditto full attacks and the like; a 5-foot step during a full attack is just a free action move, without restrictions, taken between your attacks.
With savage pursuit, it's not "you move and then attack"; without the attack, there's no movement. However, because this ability is meant to let you close gaps to people, it can't work like the Dance strikes, because this movement has to happen before the attack. It's meant to let you move up to people and attack them (completely for free; it's not a move action or 5-foot step), and it only procs when you actually make an attack.
Because you can't make the attack unless you threaten someone, if the rules text allowing you to pick targets outside your potential reach wasn't there, the ability would never actually let you move and attack someone you weren't already reaching. The movement does not happen until after you've decided to make an attack against someone, at which point there's no going back—you've chosen to attack them and get your movement to move up to them and attack them (unlike, a 5-foot step, which is taken between attacks and thus the decisions of what to attack).
There's probably a way to word it so that it works as intended without having a "phantom reach" effect, but it's a bit of a complex ability to word, for how simple it seems. I might just be missing it though... I'm gonna think on it some more. If you have any suggestions for how to fix it to be more concise (that is, the movement can't be taken unless you're already making an attack, and has to be able to be used to move up and attack someone who was potentially outside your reach), I'd be happy to make changes to the wording