At first glance, it seems hard to define him here as acting unintentionally, even if from the standpoint of punishments he is close to being under compulsion.
After all, the penalty regarding an act done on the Sabbath is meant to distance people from the act itself; if you do not benefit from the act, there is a chance that next time they will not do it for you. It is understandable that when it was done unintentionally there is less reason to impose a decree, since we are dealing with a temporary mistake, and if the doer only knew, he would refrain even without a penalty. That is not true of a secular person who does not believe; that is a fairly permanent state, and the penalty is useful there, so he is like one who acted intentionally for this purpose. The basis of “intentional” here is not the degree of blame, but the fixed and non-temporary character of the act.
Isn’t that so?

First, even if you are right, we have no authority to prohibit things on our own initiative. What was prohibited was prohibited. Second, in my view the secular person is not even committing a transgression, so once again the rationale returns to its place. A child taken captive brings one sin-offering for all the times he kindled fire.

This is not “a prohibition of our own making,” but rather extracting the underlying principle from the definition of “intentional” in this context.
After all, a secular person who does not believe is not really intentional, not really unintentional, and not really under compulsion. In order to classify him under one of the categories, one has to extract the essential principle from the category. Regarding punishments, the defining basis of what counts as “intentional” is the degree of blame and the possibility of choice. Regarding an act done on the Sabbath, what defines “intentional” is the element of permanence and deliberate action.

Even according to your approach, it is forbidden to feed him prohibited food directly by hand, unlike a non-Jew. That implies that in Jewish law it matters that he is doing something contrary to the Torah because of the intrinsic flaw in that, even if he is not blameworthy. At the very least, Jewish law does not want us to feed him in that way, and apparently also does not want us to encourage him to go down that path or strengthen his hand בכך, and therefore the penalty concerning an act done on the Sabbath is relevant to him.

No. What is forbidden to feed him directly by hand is because in such a case the prohibition is on me. The practical difference is that there is no prohibition on causing him to stumble.

It is clear that in such a case the prohibition is on you (“do not eat them” — do not feed them), but it would seem that the nature of the law of “do not feed them” is that the Torah prohibited you from feeding someone who belongs to the realm of the prohibition, since the result of the act is not good in the eyes of the Torah, even if we say that they are not subject to punishments, or even if we follow your unique approach that there is no actual command upon them until their eyes are opened to see the path of truth (*).

(*) And the words of the later authorities are well known: that the slaughter of a minor is valid, even though apparently he is not included in the commandment of “and you shall slaughter and eat,” because it is forbidden to feed him directly by hand, and therefore in the end he is considered included in “and you shall slaughter” — meaning that he himself belongs to the realm of the commandment, and of the consequences of transgression, even if in practice he is not commanded.

Of course they are included in the prohibition, and they are under commandment too — not as you put in my mouth — for they are obligated in the commandments. They simply cannot fulfill their obligation because they have no faith. And this is where those who challenged my article in the Tzohar debate after it was published were mistaken; see there.
And regarding a minor, see Rabbi Chaim Soloveitchik on a minor who came of age between two Passovers, that he has fulfillment in the slaughtering of the Passover offering while still a minor, if they slaughtered on his behalf. But as I said, an atheist is also like that.

If a child taken captive brings one sin-offering, that does not mean he is not violating prohibitions; according to the Talmudic conclusion in tractate Shabbat, the number of sin-offerings depends on the number of lapses of awareness. Therefore, one who forgets the very essence of the Sabbath brings one, whereas one who knows the essence of the Sabbath and acted over many Sabbaths, etc. That certainly does not mean there is no prohibition on causing them to stumble or that no prohibition applies to them. And even if they are under compulsion, that is exactly like forcing someone to work for you on the Sabbath because there is no prohibition on causing him to stumble, since after all he would be under compulsion.

In my above-mentioned article I argued that this is also the number of prohibitions; the prohibition for which the sin-offering is brought is the lapse of awareness.