My guess is that the 9V connector is an output, not an input. It probably provides power to drive the type of amplifiers that you would typically find inside those old tiny external speakers that used to be bundled with earlier sound cards. This computer probably originally came with such speakers, but you should be able to hook up any self-powered speakers or amplifier to the LINE OUT connector instead.
It looks like a backpanel that connects to an integrated sound chip, since it's positioned perpendicular to the ISA Slots.
There's a good chance that the on-board sound card is a Sound Blaster clone.
First, check the motherboard or whatever board that backplate with the sound connectors connects to and see if you can find any dipswitches and/or jumper settings with markings referring to I/O, DMA and/or IRQ. You might also spot a sound chip near there with a logo and/or part number on it that could provide you with some clues. Perhaps you could make a picture of the inside of the machine, specifically the part inside where the wires of those audio connectors lead to? If you share such a picture here, it would make it easier for people on this forum to help you solve this mystery.
If you can't find any clues inside the machine, you can just try and see if it's Sound Blaster compatible out of the box. With a little luck, it's set to the most common setting for 8-bit Sound Blasters and clone cards, which would be I/O channel 220, DMA 1 and IRQ 7 or 5. Try setting a BLASTER environment variable in DOS like this:
SET BLASTER=A220 I7 D1 T1
Then try to configure and run a DOS game with Sound Blaster support. Some games don't ready the BLASTER environment variable and will require you to specify the above settings in a setup or install program. If so, just specify the same values as you used in the BLASTER environment variable.
If you don't get any sound, try the same environment setting, but with I5 instead of I7 and/or T3 instead of T1. Just try some combinations.
All this is assuming an 8-bit Sound Blaster clone. But since it has an integrated amplifier and a 9V output, I don't think that card is new enough to be a Sound Blaster 16 or anything of the same era.
If the BLASTER setting doesn't work, then try to find a game that is smart enough to auto-detect the right sound card. Some games were pretty good at that back in the day.
By the way, if it is indeed a Sound Blaster clone, then Adlib compatibility should work out of the box, and you should at least hear music in many games without requiring any manual configuration.
Good luck!