I'll start with saying that this story is not perfect. There are a few references to manga or anime (or whichever) which we assume wouldn't exist in the world of SAO, and which therefore make no sense. And there is also the fact that the weapon skills in SAO were not supposed to work if the player held two weapons in their hands (with the exception of Dual Wielding, as we learned in the series proper) which, if true, would ruin quite a bit of this story; not to mention the whole "shop in a duel" thing.
But that is just one side. And on the other side, the references aren't so plentiful that they would disturb the experience for any readers outside of those really sensitive to this sort of thing. And the explanations given for why exactly do Sinon's skills work the way they do is one which makes sense, especially since the one weapon skill she uses might be a bit different from the rest of them and we never learned of the exact mechanics behind them. And the bit about "shop in a duel" wasn't really discussed in the original story, so for as long as it remains consistent here and matches the rest of the rules in the story (which it does), it is not a problem.
To add to that, the author of this story clearly is capable of writing as the flow of the story is good and there aren't any atrocities committed in regard to spelling and grammar (which is quite rare nowadays, sadly).
That being said, if you can stop worrying about the exact minutiae of SAO and the uncertainties of it for a moment (and know who Sinon is, obviously), give this story a try and you likely won't be disappointed.