>I think there's a fairly trivial distinction
... What's the difference between my Roku TV & my iPhone? My Roku can clearly do some general purpose computing. So is it trivially a general purpose computing device or trivially not a general purpose computing device? Let's follow your workflow.
>is the system aided by software to operate, vs is the system a platform for executing user-software
Hm, I think my Roku is a TV, and so someone would expect to be able to use it without additional software. Indeed, it has about 8 ports on the side I can plug game consoles & cable boxes into. Therefore the system is aided by software to operate. Therefore it is trivially not a general purpose computing device.
Now, what about my iPhone? My iPhone has phone in the name. One would expect to be able to make a phone call without additional software. That is indeed the case. Looks like my phone is trivially not a general purpose computing device.