Well, if we’re going to nitpick (and I do love these discussions so bear with me), the C-130 is a turbine powered aircraft just like the A-10. The powerplant is much closer related to a turbofan/turbojet than it is to a piston engine.

Yes it is, in fact. It’s a turboprop, which uses a turbine engine to drive a propeller. The turbine itself also generates nominal thrust, since a jet can’t operate without generatin thrust.