As you have shown yourself, when we want to say that we are doing something other than a specific action, we simply use negation:
In other words, I don't want to say
that this person is doing a thing
different from running. Only that he's
You see you are using negation to describe that which you want to describe without negation? This is a very efficient and natural method; that is why there aren't a great many words that specifically negate other words without using a common marker of negation: using not or non- or in- or something like that is simply an excellent tool.
I think we mainly use "opposite" words without negation in cases where two words together fill up the whole space of probable situations, so that we have only 1 or 0. Consider man-woman in the context of sexes, or running-standing in the context of a game of baseball: in these cases, there are usually two choices each, so that we call one the opposite of the other.
But if we consider man, woman, child in the legal system of the Romans, or standing-sitting-walking-running in the context of a street view, these pairs cannot be considered opposites. Whether one thing is the opposite of another it is usually impossible to say without a tertium comparationis, a third concept that serves as a common frame of reference. Note that this is often not explicit; but it is still there in the background when you think about it.
When we use negation, we are often dealing with a whole that can be divided in more than two parts; we just want to say that something is not in part A, but in one of the other parts. Only when the whole consists of two parts only, and those parts are of a similar "size" in one sense or another, does a negation make an opposite.