There is the constitutional line of succession, which Alexander Haig, the Secretary of State, was NOT speaking about.
And there is the Executive Branch Chain of Command, which found Haig, the Secretary of State, in the White House in charge because The President and Vice President were not, as they say nowadays, in the house. The White House.
Haig had a discussion later and made the mistake of referring directly to the Constitution to explain his position. He was indeed in charge but not because the Constitution said so. Rather, laws were passed creating a chain of command for the cabinet officials.
Cabinet officials are also in the line of succession to the Presidency if the President and Vice President and the House Speaker and the Pres Pro Temp of the senate were all uh, incapable of moving up per the Constitution - Don't ask.