No, it's not, unofficial actions are not immune.
Then nothing is immune, except things that are already legal and thus have nothing to be immune from.
The entire structure being given is that if something is a core duty, and you do something that is a crime while performing that core duty, then POTUS is absolutely immune as regards that crime and it also cannot be considered as evidence.
Since commanding the military is about the most core a duty can be (being explicitly assigned to POTUS by the Constitution and all), and it is possible to command the military in a fashion that is a crime, then POTUS is absolutely immune as regards commanding the military in a criminal fashion.
This is about the most overt and obvious the issue with this ruling can be. If doing a crime when performing an official duty makes it cease to be an official duty then the decision protects literally nothing because it does literally nothing and protects Trump from literally nothing. If doing a crime when performing an official duty (let alone an absolutely immune core duty) does not make it cease to be an official duty, then any crime related to an official duty is totally irrelevant as regards POTUS, barring only impeachment.
I'm still looking forward to the arguments in the future about whether or not you can impeach a former president long after they've left office (and/or impeach the same former president multiple times over different issues, even if a previous impeachment is convicted), as a requirement to make the actions impeached over no longer "official" (since only things wholly unconnected to any presidential power would be able to be prosecuted otherwise, and then only after an initial round in court to argue that point). And whether or not double jeopardy applies to impeachments (meaning you could intentionally pass articles of impeachment with a friendly Senate that you know won't convict to confer permanent immunity).