What are my options for hardwood floor scratch and gouge repair?
One option is to replace the board.

You would need to:


Cut out the old board.
Find a board that matches the type and grain of the rest of the floor
Install the new board.
Stain it to match.
Buy your dog a chew toy. :)


UPDATE

You can remove most of the old board by:


Cutting it out with a circular saw.
Using a hammer and chisel (or even a flathead screwdriver) to chip out the ends.
Chisel out the old tongue from the groove in one of the boards still in the floor.


To fasten the new board:


I would apply a liberal amount of would glue to the subfloor.
Slide the tongue of the new board down into the old groove (that you chiseled out).
Put a few face nails in the new board.
Fill and sand the nail holes.