Karma is a concept that predates the Buddha and directly translated is something like 'action' or 'deed' done with some intent. It is related to the law of cause and effect in that our actions and deeds have consequences. So called good/bright karma are those actions which result in consequences down the road that we find good and similarly with so called bad/dark or even neutral or mixed consequences.
With that background I think the crux for your question is that karma is defined as intentional or volitional actions. Karma is those actions we take with specific intents. Actions taken without any intent whatsoever simply don't apply. Intent or volition is a product of the mind so it is imperative to look at what the mind intends with every action we take.
If one takes actions with zero expectation or desire this sounds a lot like zero intention or zero volition, but somehow I don't think this is what you mean? Usually, when we give something away we usually intend some result or consequence of this giving action, yes? A good intention might merely be to bring relief from suffering in the case of giving food to someone who is hungry. A bad intention might be to cause others to praise us for how generous we are.
To clarify, are you asking about the case where we give with zero intent whatsoever - not even to bring relief from suffering in the case of giving food to someone who is hungry - or are are you asking about the case of only good intentions like the above? If the former, I think it is not a karmic action as it has zero volitional action. If the latter, then I think it is a karmic action that will bring so-called good karmic results, but the question is to whom?
One way to understand the sutta you referenced is that its talking about karmic actions taken with zero intentional volition on the part of "I-making" or "mine-making." That is, intentional actions we take that simply do not have any relation or intention bundled up with our ignorant sense of self. If we give food to a hungry person merely to relieve them of starvation with absolutely no reference to "I" or "mine", then this intentional action will have neither good nor bad karmic results for "I" or "mine". In this sense, I think it would be a karmic action taken that results in neither dark nor bright consequences for the "I" and would lead to the ending of "I-making" and "mine-making." At least that is how I understand the teaching.