Can you show a photo of it ?

When there's a speaker output but no jumpers and you can actually see the amp chip there's no turning it off without actual modifications to the card. Without any obvious amp chip on the board there's just a line out and maybe the AC97 codec chip attached to the YMF can output enough current to drive headphones and/or speakers...

Here are some photos. There are what appear to be jumpers on the right side but those are actually PC/PCI which I think is the same as SB-LINK.

This card has unbypassable poweramp on it, so you're stuck with very loud and noisy output on this particular card. With some effort it is possible to bypass the poweramp but it will take some soldering.

Can you share some insight on how to go about bypassing the amp?

There are several ways :

* Remove the amp chip and run its input pins to the output. A pair of capacitors will have to be removed too and there may be polarity swap necessary, with positive end toward the card and negative toward the output connector.
* Leave amp chip in place and simply remove output capacitors, while running a wire from input to the connector end. This will have worse performance since the amp chip is still drawing some power and there can be electrostatic coupling of its output to the new line output.

Removing the chip is the best way and if you don't intend to keep it you can just cut it off, no PITA chip desoldering process necessary.