Broadly speaking, I think "medieval" is interchangeable with "pre-industrialisation" to the layman. I don't think the average person cares to distinguish between medieval fantasy and Renaissance-era fantasy.
Again, this fantasy is set in a world like that after the Renaissance.
And you're misusing the term “layman”. While I would agree that not many people particularly care, any westerner who paid attention in grade school would know that “medieval” refers to the period between the fall of the Western Roman Empire and the Renaissance. So we're not writing about laypeople as such; we're writing about people who didn't pay attention, or later just said “fukkit” to what they learned.
Given that, in turn, this means that they aren't well positioned to understand how we got where we are, where we could be, or where we are currently being led, that's quite unfortunate. Indeed, as the story develops, it becomes clear that the author conceives of only two social orders as possible, aristocracy and the welfare state.
Uwahh, do you realise how obnoxiously pedantic you come off as? The point is that fantasy, stereotypically, takes place in a low-tech world, ie, pre-industrialisation. They were conveying that it's just another generic pre-industrial fantasy world with their comment; nobody cares exactly what era it's based in so much as the lack of more modern technology.
To a historian, "medieval" refers to a specific period of time. To somebody who is not a historian, or in other words a layman (since I have to spell this out for you), it might as well mean "old". You can lament the state of education on history all you want, but the reality is that if you took 10 people off the street at random and had them read this manga, approximately zero of them would say "this is post-Renaissance fantasy" when asked to describe the setting.
Your usage of 'grade school' suggests that you're American, but the idea that American schoolchildren under the age of 10 are well-enough educated on European history to differentiate the eras is, frankly, preposterous. There's no reason to stoop to the level of insulting people's intelligence by suggesting that they're more moronic than a child for not being that informed; as a non-European myself, I didn't learn anything meaningful about European history until I studied it in university.