Yes, because it is literally "bang, out of order" (mention, rather than use of the word bang, in the wrong order) and he is claiming it is "bang out of order" (expression of disapproval), so there are two meanings applied to the one phrase, providing humour.
No, because the result isn't another word. If it was an anagram then that might hinder the humour, because the puzzlement about about either what the random letters are (if the audience don't manage to descramble it) or why it's misspelt (if they do) serves as the feedline.
Consider if the card had said "Oh! Cling Sky" and he'd said "That's shockingly out of order". Of course it would lose a lot of its humour because "shockingly out of order" isn't a set phrase, but also because it's not as immediately obvious that it's made up of the letters in shockingly out of order.
a one-line joke,
AKA "a one-liner". Yes, though it isn't a fully independent one-liner that depends solely on the contents of the line.
a factual statement
or something else
It's also a feedline/punchline joke, though the feedline is visual.