Is a "GPS required" ILS (or other navaid-based) approach considered a "GPS approach" for alternate planning's sake when TSO-C129/196 gear is in use?
This is an excellent question.

However, since the approach you reference, KJAC ILS Z or LOC/DME Rwy 19, "requires" GPS, I would interpret it the same as a GPS-only approach for planning purposes and subject to the appropriate restrictions. Those are: either the destination or alternate, but not both can be a GPS-only approach airport for TSO-C129/TSO-C196 [GPS-no WAAS] equipped aircraft.  Both destination and alternate can be a GPS-only approach airport if the aircraft is equipped per TSO-C145/146 [WAAS].