The cable you bought is for a combined headphone and TOSLink output to regular TOSLink [headphone jack with LED at the back of it - seen on (at least) Mac laptops and some MiniDisc players.]
The device you have appears to output S/PDIF as an electrical signal (only) on an RCA jack via coaxial cable. S/PDIF can use either transport mechanism, there's no expectation that a given device will do both. The fact that you can fit the special purpose TOSLink cable into the electrical-signal-only jack will not make an LED magically appear at the back of it. Notably, the manual only illustrates RCA-type cables.
You would need an electrical to optical converter to go from S/PDIF with an RCA Jack to TOSLink. Or you need to use an S/PDIF input on an RCA jack with an RCA cable - which that device does not have.
Example, not endorsement, I've never heard of this company nor used the device, just the least costly one that went the right direction I could find in a quick search. Optical to electrical appeared to be available for half the price, at least on sale. This one claims to go either direction. There's a wide range of products/prices, so you can pay 10-20X as much to suit any AudioPhool tendencies your friend might have.
