This question is asking us to name a game based on a picture of a tentacled creature playing said game. A commenter has stated that unless we can "prove" that the game doesn't exist, it should be left open, even though the OP has said "there is no reason to assume this is a real game". This seems like an extremely broad interpretation of the identify-this-game topic. I could create a question saying "I had a dream about a game that was played on a six-sided board with a grid on it. What is the name of that game?" and it would be essentially equivalent. Is my close vote appropriate, or should I just downvote because I think it is not a useful question?
I think it should be closed and the asker should consult Anime & Manga Stack Exchange instead. We can't really help them very effectively.
It's worth noting that media regularly makes up games completely: Firefly features a card game where the actors have said in interviews they were just given cards and told to improvise; Battlestar Galactica features an equally nonexistent poker-like game. It's just really convenient making up games when they're not all that important, rather than having to learn and execute the rules properly.
The thing is: we aren't expected to have that expertise. It isn't our domain. We are board and card game nerds/experts. We aren't the film & tv or science fiction & fantasy nerds/experts with the community who've watched all the cast interviews and stuff; I only know these things because I'm coincidentally also one of those nerds.
If they asked on Anime & Manga, chances are high they'd get someone responding:
It's totally made up, the artist said so. This one character mentions the name of it on page 36 of...
We don't have the manga expertise to determine that though, we just have endless people who'll open the question, go "oh I don't recognise that game", and move on. It looks like go or shōgi of course but it isn't either of those, and it probably isn't anything.
In principle, questions are not off topic just because they could be asked elsewhere. But they are on topic when they draw on expertise relevant to what our site offers. We can't help them with our expertise; they need expertise from somewhere else.
So in this scenario: game from media with no obvious resemblance to anything that has an extremely high chance of being completely made up? It's off topic here because our expertise isn't what will solve this; there is another extant Stack Exchange site which they can and should look to for a solution. They will be likely to find it there, and not likely to find it here at all.
See, if it is a legit game, which is to say it has clear rules and is playable on or around a table, then it would become an identify-this-game question and would be clearly on-topic here. We're totally qualified to handle this sort of question and many of us would love to do so; the game having had an origin in fiction or not is irrelevant.
If, however, it's not a legit game, the best anyone here would be able to do is say "No, that's not a game." which is…a pretty crappy answer. They the answerer would then be stuck with the unenviable task of proving the negative, which is just ugh. And, since it's not a legit game, they'd not only be stuck putting all that work into the answer in order for it to be useful, they'd be stuck putting all that work into the answer in order for it to be useful to a question that is explicitly off-topic.
The problem is, there's no effective way for the questioner to know this coming in (or else they'd not be asking the question in the first place). Even if the game in question is clearly fictional in origin (e.g. described in a novel or displayed in a comic or tv show or whatever), there's plenty of precedent of such games actually being (or becoming) legit games. There's also plenty of precedent of such games just being wholly unplayable and completely made up for the story because they needed something that looked recreational. It could totally go either way.
This is something that we as a community can totally help with, since we know games including, for the most part, what is or is not actually a game, and not all such questions have a convenient other site (Anime.SE in this case) they can also ask at. However, this sort of question really sucks under the Stack Exchange model because it's not particularly answerable in a good half of the cases: We're the right community, just the wrong model. Chat would be a great place for this; the main site, not so much.
Before asking their question on the main site, expecting the questioner to put due effort into determining that the game in question is, in fact, a game (as defined by our scope) rather than just artistic license or even just a random thing-that-might-be-a-game is completely reasonable, and it probably should be closed as off-topic unless there is a good reason to believe that it is, well, on-topic.
(Of note, the reason I didn't personally vote to close that post as off-topic was because, frankly, I had no way of knowing one way or the other; it might've been a game, but then again it mightn't've. After due consideration, voting to close was probably the right course of action exactly because of that ambiguity.)
Judging what is "likely to be a real game" would probably need to be taken on a case-by-case basis; a random card game in a TV show set in modern times for example is far more likely to be legit than a random card game set in the far-flung space-faring future. Similarly, it's probably reasonable to believe that an author who has a history of presenting fully-developed and playable games (Nobuyuki Fukumoto's mahjong variants come to mind) has done the same in their other works, whereas a first work by an unestablished author wouldn't be given the same benefit-of-doubt.
Either way, I wouldn't downvote the question; it's still useful — I, for example, would love to know if the Houseki no Kuni boardgame is a real thing — it's just a question of whether it belongs here or somewhere else, and how best to ask it. Even if the only "response" they get is an off-topic close and a comment-discussion that this is probably not a real game, even that is still useful to future visitors who also want to know the same thing.