That is what I thought. Most likely the lot is situated in a place that makes this common. Enter lawyers at left.
The issue with running a cable across a “driveway” is that it has to be “marked” with either flags or a hanging sign. Otherwise it is not visible. And, at least in my area, this applies to private ways as well. YMMV.
That said, when I was riding...”cut throughs” were always more concerning than just pulling out onto a road because pedestrians and other traffic were not “expecting” you to pop out there.
How much time are you really saving anyway?