How do I fix a good size gouge in my faux wood vinyl floor?
Obviously the best bet would be to replace the tile, if it's tile, if it's sheet vinyl well...
If you have ANY of the material left over, you can cut out a patch and replace it, use a liquid seam sealer to make it look good...

You can purchase a vinyl sealer, that will basically attempt to fill in the gouge, use of lacquer thinner is required, as this is going to clean the area first...

You can purchase wood putty, or a wood crayon at your local hardware store. I used to work in Lowe's flooring department. They also sell repair kits, but you would probably be better off matching it yourself, start low.
So clean it up, broom and mop. Neutral cleaner if necessary, 

Apply the putty or crayon or whatever you will use to fill the gouge. They sell markers that help you fill in the extra stuff colorwise...You can set and let dry this way, wipe it clean and repeat the process, if necessary...OR...

you can apply wax to the whole floor, this will seal up and if you go low-gloss, you might be able to mask up the imperfections in a similar process as would be handled by a flat paint on an ugly wall.

Minwax has a reputable putty here