Jazz historians often commit a terrible crime - criticising something for what it isn't rather than appreciating it for what it is (to paraphrase my dearly missed friend and mentor Len Barnard). I've read countless jazz history books wherein quality 1920s musicians receive patronising assessments due to their alleged inability to 'swing', usually defined in the sense of 'swung eighth-notes' as played by Basie in the late 1930s.
I think musicians originally used the word swing to describe a powerful rhythmic energy, and that can take many forms. King Oliver's Creole Jazz Band swings in this sense. So too does Louis Armstrong's Hot Seven, romping through Potato Head Blues, or Bechet's recording of Sweetie Dear. In each case, the combined, cumulative effect is what is important, not whether it fits a certain definition.
Here's a powerful example from The Little Ramblers in the mid-twenties - hardly swing a la Basie, I feel Adrian Rollini and Co achieve a combined rhythmic drive here that is awe-inspiring: