The simple answer is that the game was not released on January 31st. I don't know exactly when it was released. I tried to figure this out about 9-10 years ago, and found references from January to March of 1999 as the American release date. Nowadays January 31st seem to be accepted fact all over the Internet, but it couldn't have been. Primarily due to file dates on the discs...
Regarding file dates, there are lots of false information in this thread. The date stamp on files on discs are from when when digital files were created/edited. It is NOT from the time a factory manufactured disc is molded (or pressed, or whatever you want to call it). Molding a disc is just plastic being molded with pits and.. well, no pits. How would molten plastic know the time? The process only replicates the exact same data that was already mechanically etched into the pressing plate.
The date is also not from when a CD-R is burned. This is also a physical process, which again, only replicates the exact same data that was already there. A laser burns away a dye inside the disc. No new file dates are created. (However, the computer burning the disc could perhaps generate new dates if it creates a temp file to burn? I'm not sure.)
The retail game and the Trade Demo as shown above are factory manufactured discs. The file dates, which are the same for all files on each respective disc, are most likely from when the files were transferred to the computer which was used to create the master CD-R (which was later used to create the glass master, then metal stampers, then discs).
There is also a third disc, which is a little earlier than the Trade Demo. A review code on CD-R (for those that are not aware, CD-Rs/DVD-Rs etc were and are used by the industry to send out previewable and reviewable game code to magazines (and a lot of other purposes). The file dates are from January 6th. So this was was sent out for review, as was the Trade Demo a little later, from the 16th. If the game was releases on the 31st, nobody would have had time to review it before it came out. Remember this was in the days of magazine deadlines.
Considering the dates on the review disc and the trade demo, February 9th sounds perfectly sensible time to start creating the master disc.
I can also add that January 31st 1999 was a Sunday.
To answer some specific points:
The dates on a disc are created when the disc is burned, not when the files are made
I just want to stress that this is not certain. Try to burn some old files to a disc yourself.
There are not just two shipments of the game worldwide of the "original" and "greatest hits" versions. Products are manufactured and shipped in waves.
Absolutely, but if they use the same master to create pressing plates for each repress, a disc manufactured five years later will still say 1999, because disc molding does not change the file date. With music CDs they often seem to create new masters each time they re-release it, but games were usually reissued using the same master.
It is also entirely possible that (for some reason or another) the machine(s) that were generating the discs were operating on an inaccurate date/time setting.
Nopes, as mentioned, that has nothing to do with file dates.
The computer which changed the file dates could of course have been on the wrong date, but we also have the Review code and the Trade demo from the 6th and 16th respectively. They wouldn't send those out so close to release, they would have done it sooner. If February 9th is the wrong date on the retail disc, then the Review and Trade demo discs have wrong dates, too.. Which is unlikely.