Toriyama's statement there and before are not in contradiction with each other. He said in that very article that the major story structure being the same in the game, which is true. There's very little deviation from the original storyline as all of the major events are there. It's a different continuity though and that explains the additional elements and interactions such as Jessie going to the depot to get different explosives and all of the other stuff.
For one thing, the
core story structure is only there on a surface level. Sephiroth is handled in the opposite way, and many events are "intact" only in a checklist fashion. They still fight Reno and escape from the church, we just have to ignore what happens in the church in between.
The group still storms the Shinra building, the president is murdered and they escape, we just have to ignore Barret, Hojo with the ghosts, what happens to Biggs, Wedge and Jessie, and the entire ending of FFVII itself and the resurrection of Zack shoehorned in Disc 1.
By just using that logic, you can do whatever you want with the plot. That is garbage logic.
Second: the fact it even implies the possibility of "another continuity" means a major retcon, so we're already off to reboot-zone.
FFVII had no time ghosts, no time-travel, none of that, Sephiroth didn't travel time and knew a lot of things but not how to travel across dimensions and time, saying otherwise is dishonest, it's all new.
Third: it's a remake that directly addresses the original as a reality that either existed and it's been rebooted or a future timeline they want to escape and that makes this pretty much a new reality in spite of the original one, so it's more or less a sequel.
Whether you want to call it a spin-off, a preboot, a premake, a seboot, sidequel, a rebootake or a sequelmake it really, seriously doesn't matter: FFVII relies on too many small things to work, retconning Zack and Aerith's death won't keep the major story structure so we're discussing a done deal.
Also, you would have to explain why would Sephiroth, the guy that in the original only lost because of Aerith's hail mary from the lifestream, lose now? If anything I'd expect to see them all dead in Kalm since they can do absolutely nothing to stop him now.
With a focused, unrestricted Sephiroth I'd expect to see way more casualties, not less, wasn't that what they meant to do in the original anyway, just keep 2-3 characters alive?
The only way to fix it would be a remake time that actually chokes, as in "this new timeline is a fiasco, Sephiroth played us all, we need the old one or we're all dead". I don't think Nojima and Nomura have enough common sense to pull it off.