How do I read SNx4HC244 logic diagram?
Am I mis-understanding something or is the data-sheet wrong?


Yes, the current version of the datasheet is wrong.

Notice the text "SCLS130E" on the header of most pages in the current datasheet, which tells us that it is revision E. The mistakes which you highlighted were only introduced in the latest revision to that TI datasheet, when it changed from revision D (August 2003) to revision E in May 2016.

Here is the equivalent, correct, diagram from the previous revision D datasheet - see the header text "SCLS130D" below: