Tried it out on my Win98 machine as well as on DOSBox. I couldn't get DOSBox to work at 1600x1200. It complained about not having a compatible VESA driver for that resolution.
1280x1024, Win98SE, Celeron-1400, 440BX, Voodoo3 3000 AGP
Low: 33 FPS
High: 57 FPS
Average (walking around with no enemies on screen): ~45 FPS
1280x1024, DOSBox 0.74 on Win7, i7-4930K @ 4.6GHz
Low: 45 FPS
High: 140 FPS
Average: ~75 FPS
So based on that, I'd guess that DOSBox on a fast machine would be able to handle it smoothly at 1600x1200.
The 1.4GHz Celeron would probably average under 30 fps at 1600x1200, but I'm guessing that most P4s above 2GHz would handle it fairly well.
Standard Def Rigs
Super P3: PIII-S @ 1.63 GHz/FSB155 | 2GB DDR-310 | 6800GT AGP | 500GB 7200 RPM
Super G4: 2x PowerPC 7455 @ 1.5 GHz | 2GB DDR-333 | 7800GS AGP | 300GB 10k RPM
Super G5: 4x PowerPC 970 @ 2.5 GHz | 16GB DDR2-533 | x1950XT PCIe | 512GB SSD