I think the most objective way is to consider the order being the order of the very first release of each entry.

For the example of Final Fantasy, this would (likely) be the Japanese original releases that determines the release order, unless a certain release was before the Japanese release, then that counts instead. So even though several games weren't originally released in North America, that wouldn't matter, since it would be based on Japan. Unless you want the sequel-order to be per region.

But perhaps this system would be the best suited for games where the order is clear.

Release date is the least likely to be contentious since it's objective and inarguable. It would be great to see an entire series and its entries in one place!

If I am going back to play a series I didn't play when the games were released I might do it chronologically. Each series' wiki will probably have a timeline that can be found but I still think its useful information that can be held here.

Because the site already has a franchise page that can be sorted by release date, maybe there could be a data field for the games chronology that could then be sorted in the franchise page. I guess with games that don't have dates like Zelda a numerical value would have to be put in front of the 'era' for it to be sorted.

Personally, release date is what i look at when thinking of play order. When I play a game that has a prequel it makes the prequel better if i play it second instead of first because I will see references to the future that I remember from the sequel. and as a few of the comments have stated, having a series release timeline would be usually more important than a story timeline, though both would be nice.

Overall I think the release timeline should be auto-made by the system but then the story timeline could be updated by contributors afterwards.

I was thinking in both ways to link the games: canonically and by order of release. Both could be linked and the user could have something like "This game was released after x and before y" or "This game is a sequel to x and a prequel of y". The release factor could be calculated automatically inside the data of release of a game series, using the first release date of each game, so it could be dynamic for when a game gets some information updated if a date is wrong or this kind of situation. About the canon linking, it would need a manual linking, as the contributor would have to think story-wise.
If the canon linking is too difficult to maintain as a data point, at least the ordering by release date would be good to have on the game page, as it is doable with the data already in the database and dynamic generated. Portuguese Wikipedia has that for some games (albeit the English one doesn't) and it is a neat feature.

Totally understand the concern. It generally becomes a problem when you have series that either abandons the numerical release like GoW, or titles that pick and choose their timeline events like the dev's example of MGS3 or Street Fighter IV-V.

I would actually like to have both, but in a sense we "should" already have sequential release in the data, so long as the release dates are entered correctly and the Series is tagged in each title. We simple lack a visual UI that displays it. (Like a link that currently states if a game is an Expansion of X Title, but for Series.)

The only thing that I see that would require extra attention would be like in your FF6 vs FF4 situation. In that case for chronological timeline, you would probably want to omit "Versions" and go off the original release.

Something like the following link would be preferable, but would probably have to have some sort of toggle between sequential release and story timeline.
https://tinyurl.com/y2qbwmor

Although Series lets you browse these items already, it makes sense for this to be accessible as DLC items