Possibly the game engine sound section is poorly written and struggles with two sound cards present even though you are picking just one, is all I can think of.
Which game is the worst ?

Incoming is the easiest to test. I have it paired with a Riva TNT. It's buttery smooth on either sound card but a choppy mess when both are installed at the same time.

Pretty sure running onboard and a pci sound card being both enabled is not a good thing to do.
Even though Device Manager may not complain about it, I am pretty sure the motherboard chipset and PCI controller are not going to be to happy about it.
Especially on these older motherboards (Since you did not list the motherboard).
They are going to share resources even when one is not directly in use at the time, that is windows 98 for you.
And a Celeron certainly does not have the oomph to cycle resources on the PCI bus for that.

But the fact that you literally disable one or the other (Bios/Device Manager), and the issue goes away pretty much explains what this.

I found the cause and a fix for this. I had left both legacy sound emulation devices enabled in device manager during testing and didn't think much of it, because they did not have conflicting configurations or resources and I wasn't testing a DOS game. Disabling either legacy sound emulation device (so that there is only one) fixes the issue.