Where in the world are cabinets more often referred to as cupboards? In the world of ESL (English as a second language).
I teach English to private students in my spare time and in all the textbooks I have in my possession, be it for nursery school children or adults who are taking advanced level exams, the piece of furniture that the OP refers to as cabinet, is rarely mentioned. In fact, I don't think I've ever seen the word cabinet in any ESL textbook.
Instead, it's cupboards (unless it's a trophy cabinet); wardrobes (never closets); sofas (never couches); and bedroom or kitchen dressers (never hutches) etc. This might well explain why the non-native speakers in Europe were all familiar with the term cupboard but not with cabinet.
And I confirm @Dan Sheppard's statement that the above linked terms are standard British English terms.
I scanned this page from an English coursebook with its accompanying picture. It's taken from Elementary New Headway English Course by Liz and John Soars; published by Oxford University Press. This edition is dated 2000
Headway was first published in 1986 as a two-level course and its
integrated syllabus, explicit grammar rules and user-friendliness made
it work equally well in the hands of both experienced and novice
teachers. Now in its fourth edition, its continuing popularity has
resulted in 70 million copies sold and it is estimated that more than
100 million students in secondary schools, tertiary and teacher
training institutions in 127 countries have learned English using the
Not all kitchen cupboards in the UK or for that matter in ESL textbooks are like the ones shown in the image above. There is another type of cupboard, the tall freestanding unit containing shelves complete with one or more doors. In New English File Elementary by Oxford University Press, 2008, there is an exercise where you have to match the words with the pictures.
Take note that AmEng terms such as; stove/range, faucet, couch/loveseat, and cabinets=cupboards, are rarely found in British English coursebooks nor taught to learners. In my experience Italians tend to be taught English by non-native speakers who were themselves taught exclusively in British English. The ubiquitous AmEng terms such as: candy, cookies, (french) fries, soccer, elevator, and truck, might be taught alongside sweets, biscuits, chips, football, lift and lorry but strangely enough, AmEng named furniture is normally excluded and I don't really know why. Generally speaking, the teaching of furniture vocabulary is relegated at elementary levels and rarely revised or expanded at higher levels.