However unnatural it is, D&D combat and movement *does* happen with stop-motion. Two opponents stand 15 feet away from each other. If they are entering melee combat, one of them needs to close that distance, and that one gets to attack first.
This is factually incorrect. We
use stop-motion to represent movement, but the movement
itself is continuous within the game world. If two opponents are facing each other across a short distance, then approximating that the faster one to act can get
to the other one before that one moves even
five feet is
sufficient for us to resolve their interaction.
Plus, the word Immediately is used elsewhere to have the meaning I am ascribing to it.
I'm not sure that's a convincing argument, but did you have any specific examples in mind? It's just a normal word in the English language, so there's no real reason to expect it to hold some special definition as game jargon.
Do you believe that long jumps are *expected* to have the run-up at the end of the last turn? That to me is a big assumption, and it also is not paralleled by other actions in the game, so far as I can see. If that's your interpretation (and that the full benefit of these shoes for someone with 15 strength depends on that assumption), then I'd want some sense of why you think it's inevitable, or why that makes better sense than my alternative.
I believe that long jumps are
expected to take place outside of combat. I seem to recall that, if you
do make a long jump in combat, then excess distance of the jump beyond your normal move speed carries over onto your next turn; but I can't find anything about that in the Basic Rules, and it's entirely possible that I'm remembering that from a different game.
It's also possible that they just
don't expect this situation to come up under normal circumstances, and the line from the item description is simply intended to keep the game moving. Kind of like how some rulesets would just say that a wizard
can't wear plate armor, and later expansions of the ruleset would say that they
can but it would cause all sorts of penalties. It's just two different ways of describing the same sort of behavior, depending on how much detail you want to worry about.