She just assumed control in the power vacuum that was left following Tommen’s death. Once he went for his impromptu base jump, there were no Baratheons left (can’t remember when Myrcella died, but assume she’s out of the picture too), if it had happened during a time of peace there may have been a Great Council to choose a new king as has happened in the past, but it wasn’t a time of peace, so the Queen established herself since all the levers of power defaulted to her control - the Kingsguard were sworn to protect her, the royal household obeyed her command, she lived in the palace etc etc.