^ Nice looking cable but pretty expensive. You could probably find a 5 pack on Aliexpress for $2, or paying the US importer markup...
(1) 3.5mm Stereo Female. (2) 3.5mm Stereo Male. Connector: Nickel plated. Cable: Black PVC jacket, OD: 3.0mm.
www.ebay.com
I'm sure there are others even cheaper on ebay if you keep looking, but to avoid the problem with the first cable tried, avoid those that mention mic, or have the two male plugs with one green and the other red insulator rings, or that state they have a 4 contact female socket.
Also, depending on what the output stage is like on each PC, the result is unpredictable whether having two systems constantly wired in parallel, will degrade the sound. Ideally instead of a splitter cable, you'd get an A B audio switch splitter or just DIY wire one up with a DPDT switch on the signal wires to isolate them. If either system is unique in having a floating ground (anything operating off a 2 contact wall plug like a laptop), then you might want to isolate the ground leads too.