The study is “self-control” which means patients are compared before and after the exposure (vaccine or covid) for the outcome (myocarditis). So there is a control - the control for each person is their pre-exposure selves.

If you want to argue against the article I suggest considering the bias of being 1 year older after the exposure than before it. For a large population that might matter for myocarditis incidence. I suspect they have corrected for this however.