Well, the basic meaning of kettle is ‘a vessel, usually of metal, for boiling water or other liquids over a fire’. Originally a kettle was essentially what we’d now probably describe as a ‘cauldron’, which is what its German cognate, Kessel, still means. (That’s why a ‘kettledrum’, a metal cauldron-shaped drum, is so called.)
There are all sorts of kettles: fish-kettles, camp-kettles, dye-kettles, et cetera. Originally the thing we boil water in for hot drinks was called a tea-kettle; but over time it became the only kind of kettle in most people’s kitchens and so the need to distinguish it from other kinds of kettle evaporated and the qualifier was dropped. I can’t have been the only person puzzled as a child to hear the phrase ‘a pretty kettle of fish’ and wonder: who would put fish in a tea-kettle?
I’ve no idea what the kind of kettle these people are frying their chips/crisps in looks like, but presumably they mean that they are making them in (relatively) small batches by putting the raw potato slices in a single vessel and scooping them out when done, rather than on a rolling production-line process. Whether that should make them nicer I don’t know: but it sounds reassuring, in the same way that it does when the makers of speciality brands of gin and whisky tell you that they make them in pot-stills.