How to solder speaker wires back to pcb (Switch)
Your connector is still there. It's attached to the cable, but ripped off the PCB.
That's why you've got copper red-brownisch rectangles at the bottom of your plastic piece, and missing on your PCB.
Since it's ripped off, there's noting to solder it on to, so:

Is it possible to solder directly to the motherboard?

Not in general.
You will have to figure out to which contacts these cables originally connected to. If you're really lucky, it's the two narrow silverish ones, and not the two contacts you've ripped off.