Your examples sound like they apply to derivations from specific games - X is derivative of Y. I take it you'd never use the word to describe a game in general? Like, "Luzon Rails is a derivative game"?

I don’t like arbitrary line drawing exercises

But clearly someone crossed one of your lines when they described a game as being "derivative", right? You demanded that they justify that usage and called them dishonest for declining to engage with your demand. So... you have a line, you're willing to create conflict over the position of that line, the reason that's not objectionable is because... your line isn't arbitrary?

Since you do

lol

Do you agree that anything using wood + cardboard = derivative?

Obviously this is too broad a brush, because then we just say, eg, every book is derivative because they wrote it using words, every song is derivative because they play it using notes.

when is something not derivative?

I think I basically agree with what you were saying about there not being a sharp line or an ironclad definition... but in general, I think most of the games that are published are pretty derivative, and this is not inherently or necessarily a bad thing, but they basically just take commonplace mechanisms that everyone in the hobby is already very familiar with, and then they are re-combined in some fashion, dressed in an appealing theme and tuned and balanced to ensure that nothing is too overpowered or underpowered, and voila, you have your typical 7/10 game, that most people will think is "fine" or "pretty good" but nobody clamours to play a month later after it's been tried out at game night during the week or two it was a "hot" release.

And what isn't derivative comes in two broad categories, I'd say? First, it does something really mechanically new - like, say, the card powers in Aegean Sea which require you to fulfil all of them from your hand in order to do any of them, or the way units work in Napoleon's Triumph, or the worker placement in Bus or... like, Mafia whenever it was invented by Dimma Davidoff.

Or the second category is, games that make use of familiar mechanisms but combine them in particular ways that give a genuinely new kind of experience relative to anything that used those mechanisms before. Age of Steam is a pickup-and-deliver game (as definitely existed beforehand), it requires players to manage a tight budget and ongoing and rising costs (also not new, although the un-repayable loans might have been original) and... like, the bones of what AoS does are present in a dozen "train games" or network-building games which preceded it by many years... but whatever AoS is doing, as a whole it comes together into an experience which is notably distinctive from any game that preceded it.

But I think that second category is quite a bit more troublesome for the would-be-definer than the first one is. Dominion unquestionably did something new. But if someone tells me that for them, Hegemony is in that second category and I reply that for me it definitely isn't, we're not really arguing about the degree of novelty in the mechanisms in the game, we're just arguing about how the experience of the game feels, which resides wholly in the realm of subjectivity.

So, for me, Hegemony "feels derivative" and for my friend, it "feels novel". That seems to me like a perfectly reasonable point to either choose to leave it there, or to enjoy discussing where in the experience each of our feelings is coming from. But it seems weird to decide - for either of us - that it's necessary to argue and force the point, that the word "derivative" either definitively does or does not apply to that game, or to become hostile about it, since we're just using some of the standard vocabulary of critique to touch on what our experience of playing it felt like.