the t15 is not powered so you would need an amplifier of some sort to even use the speakers with any device. the psw10 is powered so it can receive direct input.
i believe the speaker in/outputs on that model are just for better wiring arrangements if you look at the manual as they show the receiver outputs connected to the inputs and the outputs on the sub connected to the front speakers. i would ignore this for your needs likely.
assuming now that you have an amplifier there are a few basic ways you can often connect:
A) if you use a receiver or amp which has a low level unamplified subwoofer jack or aux output that can get used at the same time for a sub you could connect the sub up to this and just have a single connection to the pc. likely you will be using a 3.5mm to rca cable but it depends on what input the amp has (some have 3.5mm, some have rca). if you had a receiver it would be via hdmi, optical, coax or rca normally.
B) if you have an amp without aux output then either you would need a splitter on the pc 3.5mm output with one side going to the amp and the other going to the sub. not an issue since your sub has L/R rca inputs but you will need 3.5mm to rca adapter cables likely for the sub and amp. on some soundcards and software you can instead connect the 3.5mm for front channel to the amp and another to the cen/sub and use this for the subwoofer and changing your settings so that the sub fires seperately than the front channels. this mayi not work on all systems but may work for you.
whats the difference? by default pc 2.1 systems use the L/R inputs and fire based on the front speaker content but only for values below a certain frequency. having it connected via separate ports (like 5.1 pc speakers do) separates the signal on the pc side instead of using a low pass filter inside the sub. either way technically works but you might have preference for one or the other.