You are correct, that the King is not explicit in this, he cannot be, he's a constitutional monarch. However, the subtly is thick, and it's not hard to read between the lines, that he is thinking the government of Sweden has failed Sweden. He represents the government of Sweden, and when he is indirectly apologising, that's the statement he is making.
And who is liable for the government in the end? Prime Minister Löfven. I think it's hard to read anything else between the lines here.
Even assuming that's true, why should anyone care? Why would someone's family line give their opinion about the coronavirus approach more value than anyone else's?
I'm not Swedish. I'm from one of those full-on democracies without a monarch, so take this opinion with some salt.
The king isn't an infections disease expert, but he's not an idiot, and he can get any experts he want to tell him what's going on. He's also the one person "in government" who can speak truth about the prime minister without fearing the prime minister's wrath. This lets the king be the one who can say what needs to be said when nobody else will say it.
Non-swedes have to understand that our prime minister does not have the power to call for a lockdown. It would require a change in our constitution, which can't be done in a hurry. (there is legislation being worked on to address the cases the shortcomings of the law but it is not being rushed)
Our PM also doesn't have the authority to tell our public health agency what to do, this amounts to ministerial governance, which is illegal [1]. (if the US would have such a law, for example, then we would have seen a lot less involvement of POTUS)
And re our king: he's (arguably) not an idiot, but he's not very bright either. We generally don't take his opinion seriously.
If you get a job, then it doesn't matter who your family is or if you're the best person for the job(!). If you are lead architect of your company, your job is to give directions etc.
Same thing here. Doesn't matter there's others that could replace the king is his job.. he's the current one with that job, so we listen in a way that takes his position into account.
I confess I come from a country that has so little respect for that job that we abolished the position, and I don't know much about Swedish royalty. What qualifications, knowledge, authority, responsibility are associated with that job? And considering that, how much respect does the job deserve?
Because they monarchy is an institution that represents the nation itself and is its unifying symbol. It's not the family but the institution that matters, it has considerable public support and when they speak, which they usually don't, it matters for that very reason.
As I understand it, in Britain by law, the monarch only may prorogue or dissolve Parliament on advice of the Privy Council, and further that the legal effect of such an act by the Crown is dependent not only on the advice of the Council but on the legality of that advice, which can be struck down as unlawful by the courts negating the effect of the order; it is a power of the Queen (or King)-in-Council as the power to create law is of the Queen/King-in-Parliament.
I would be surprised if the monarch retained greater independent personal authority as Queen of Canada.
And who is liable for the government in the end? Prime Minister Löfven. I think it's hard to read anything else between the lines here.