Viande and fromage ARE countables, (ex: "des viandes froides", "des fromages bleus") but in this case it means we are not eating ALL OF IT. But the vegetables are eaten whole. "de la" and "du" means "some" (as in part of) You eat only a piece of a cow, and only a few slices of cheese (not the whole wheel), whereas you eat a whole carrot and a whole potato (for example)

It's the other way round. 'Viande' and 'fromage' are used as uncountable nouns here and are therefore in the singular form, while 'légumes' are countable, and therefore in the plural form with an 's'. "On mange de la viande (uncountable, singular, feminine) du fromage ( uncountable, singular, masculine) et des légumes. (plural)" It's the same as in English - some meat, some cheese, some vegetables.