Well, as the song goes
Well, you know November has come, and it’s gone away.
I’ve been waiting to make that reference since I saw the table of contents, don’t judge me… Also, lyrics online say that it’s “when it’s gone away”, so it doesn’t even make sense.
My guess may be completely wrong (or already proved right where the club is), but I think
they are all on different timelines (which is why there are so many students not attending school “at the same time”). That also explains why マサムネ has games that are slightly ahead of こころ, more than that he is betatesting them (although it might also be the case). I would not be surprised if アキ’s family name was 喜多島 (could be フウカ as well, but there was nothing about her voice, and her description matches アキ better, I feel), which would explain her certainty about the fact that something happened to こころ (as well as the weird interaction they had when they first met and she said she is also from 雪科第5; also the tea bags she brought as present).
So, if that’s the case, some of them already met 
(I’m only halfway through the chapter, though, but I couldn’t stop myself from posting)
Edit: I feel that my theory is immediately confirmed by the discrepancy in class numbers. However, that makes it sound like フウカ is from the past, so maybe she is 喜多島 after all?
Edit2: Oh, there was also the hint that スバル was never compared to Ron from the Harry Potter series. If he is from the future, that series is probably a bit too old at that point. And フウカ had never seen the chocolates こころ gave her for her birthday despite the fact it just comes from the combini. I guess the closing on the 30th of March is because one (or more) of them is on a leap year?
Edit3: Their conversation is making it painfully obvious. If it’s revealed by the end of the chapter, I guess I will just look stupid. 
Edit4: okay, no reveal, good. Anyway, compared to こころ, フウカ is in the past and 嬉野 is in the future (I think he didn’t register 喜多島 as pretty since she is too old in his time). Not super sure about スバル and アキ. They know the same shops that こころ is unaware of, but that might just be because they live nearby. Meanwhile, アキ doesn’t know カレオ, which is fairly recent for こころ, so アキ is either in the past or far enough in the future for it to have changed name (or closed).