.. concrete slab floor. Built new stud walls inside the new ..foundation.
This
means these stud wall are around 4 feet from the original pony stud
walls and original foundation.

Question. How do I insulate these new basement rooms (game room,
bedroom, office) to meet code?

With mine, all they did was place FG batts between the studs (friction fit)
and then cover with 6 mil vapor barrier, and Tuck tape (red tape) the seams.

When running the wiring (before insulating) also use vapor barrier box
"liners/barriers" pictured he

http://store.drivingstrategicsales.c...ie r_1986.htm

Various styles/shapes for each "box" application.

Overlap the liners with the vapor barrier and red tape the seams. Once you
pull the wire thru the liner (you'll have to make a small hole in the liner)
seal the hole around the wire with something like red tape, caulking, or
minimal expanding latex foam. After thats done, you can install the boxes
(nail on/screw on), feeding the wire thru from the back