idk if it's based on the korean system but maybe he's considered a part timer b/c he's replaceable/being a cashier is pretty common despite the world (tho as the protag/mc he will be important later lol), and not like a 'manager'/slightly higher up job as opposed to going to college/specialty training for a specific job
Part-timer is literally someone that 'works part of the time'. A 12h work shift 7 days a week can only be a part-time work if the weekly full-time work is above 84 hours, because that is what the word 'part' means. A certain portion of the whole. 84h isn't considered full-time work even in countries famous for exploitative work (although obviously, does happen in practice).
Every type of employment has their own name. Temp contract, stand-in contract, full-time contract and part-time contract are world-wide names that have one, specific meaning, because they literally say what they are about in their name. In no way, shape or form can a 'part-time' be longer than a 'full-time'. It makes no sense in language and it makes no sense in math. It's like saying that 40 is a larger number than 84, which is absolutely impossible.