The only thing that is 2002 is the GPU out of it.
Even the Audigy used has 2001 printed on it, which would be close enough.
As for DOSBOX, that's absolutely out of the question.
If I really wanted to nitpick like you, even a few elements of OP's build above aren't exactly period correct - PSU, DVD burner, Noctua fans, USB+fan controller, and there may be more to name.
A true period correct build would use a 2000s PSU and not a Corsair CX450M from 2010, a CD-RW or DVD-ROM drive at best (no burners), no Noctua fans but instead classic 1999-2000 fans, no USB+fan controller, and an proper IBM Deskstar or equivalent spinning hard drive instead of any form of solid state drives (this includes SD/CF cards). To put it bluntly, all 2000 parts with no new PSU, DVD burner or solid state storage. Because that isn't 2000s either.
"Enter at your own peril, past the bolted door..."
Main PC: i5 3470, GB B75M-D3H, 16GB RAM, 2x1TB
98SE : P3 650, Soyo SY-6BA+IV, 384MB RAM, 80GB