I think it depends on the type of rules... sports might be more Te, as the rules don't really have to be logical at all. And science/math would be more Ti, at least philosophically. And you might consider some rules to be Fe if they're purely to promote interpersonal harmony, and Fi if they're to keep to a set of moral standards.
Te is still a kind of logic, but it's more to do with how something functions. It's dynamic. Like how to operate a machine for instance. Or how to run a business. "How to..." logic.
I think with Fe/Fi... rather than requiring strict adherence to rules, it's more like there's a general moral atmosphere of what is and isn't ok, and that is enforced socially. So it's a bit different from "Do this to result in this. Do this and receive a penalty.", it's more organic rather than mechanical.
I think Te in sports is more about the "gameplan". Picture the coach being like "Ok, so here's what we do: you move here, then pass the ball over to this player, and then we go down the field..." or something like that. Not all sports will require a Ti mindset, but I think many will, because you're constantly navigating within the rules, and having to model your behaviour based on the ideals of the sport.
Fe does have a similar thing to rules, which is code of conduct. To Fe, there are just certain ways you conduct yourself. Maybe you conduct yourself differently around one person than the next. So this would be different from the rules I'm referring to in the OP which are like... things you have to do, or else you've committed a fallacy/infringement. But I suppose a code of conduct is a kind of rules, and so too are values, and so too are procedures.
So then, what would be a better term that describes the overlapping elements of sports and science, that aligns with Ti?