I saw the Manifesto and I didn't see any socioeconomic political theories, just an apology to the police but "it had to be done."
If it said "The system of privatized health insurance is evil as a result of failure of legislation to restrain the actions of an industry" THEN that would be political, but it didn't say that at all.
My understanding is that Luigi did not publish the manifesto, and that it was discovered by others later. If that's true, then the manifesto itself is not particularly relevant to anything criminal. The message on the bullets could be considered relevant, but I don't see how that alone would be proof of intent to terrorize.
Obviously the problem is more complex, but I do not have space, and frankly I do not pretend to be the most qualified person to lay out the full argument. But many have illuminated the corruption and greed (e.g.: Rosenthal, Moore), decades ago and the problems simply remain. It is not an issue of awareness at this point, but clearly power games at play. Evidently I am the first to face it with such brutal honesty.
He explicitly states that he does not have the "space" nor the qualification to lay out what you want him to lay out, but he pretty much says what you said he should've said for it to be political: "Privatized health insurance is corrupt and greedy, we've known it for a long time and nothing has been done to prevent or stop it, thus I took a more violent approach to do something about the corruption and greed."
But the reason why they think it had to be done still matters. "This CEO wronged me personally" and "the systemic oppression made me do it" contextualize the act in a very different way. The reason he did this is why it's political. If he had done it because he had a personal vendetta against the CEO or he had some religious beliefs that made him do it or if he was just insane, then it wouldn't be a political reason. But he did it because (paraphrasing his statement) he saw an unopposed corrupt system that needed to be opposed. That is a political reason.
If the intent of the killing is to change the system or have political outcomes, then it is political.
We have no indications that Luigi wanted anything other than one or maybe a handful more dead CEOs. That does not have political outcomes. Nothing has changed.
Because he considered them evil parasites for the work they're doing. Work that is still legal now after he killed one, because killing one doesn't have any effect on the governing laws and overarching system.
You said intent not outcome. Him killing only one and it "not having any effect" is an outcome. His manifesto doesn't say he intended to kill only one, his intentions were against the system not a single individual.
Looking at the outcome and saying "that wasn't political" is like saying Jan 6 wasn't political because they failed to overthrow the government.