
The word 'twizzle' for 'twist' or 'rotate' is known as East Anglian dialect at least since 1830 (OED).
Twizzlers achieved notoriety in 2005 as an example of the mass-produced, high fat food that TV cook Jamie Oliver wanted to remove from school dinners. The makers pointed out that Twizzlers were merely an odd-shaped sausage, no higher in fat and salt than other sausages, but the product was discontinued.
Compare with the French/North African dish 'Spirales de Dinde' (Turkey Spirals).