On-demand is what it says. You are able to request a re-play/re-transmission of a program when ever YOU want to (on demand). A live service is clearly not the same. You are limited to start watching a program on or "shortly after" the time they broadcast it (live).
If you want to think about it another way, I presume (having not researched "live-restart") that the broadcast stream is buffered in the receiving equipment. The equipment still had to receive it LIVE in order to then buffer it, right? So, by definition, that requires a TV license.