They are real wood, or at least the doors are.
You can't stain over varnish. A better way to go would be as follows:
Any areas where the varnish has worn through, sand with 120 grit sandpaper to get it clean. Then stain those spots with... (looks like Golden Oak or Honey Maple) whatever closely matches. Then touch up the varnish with Minwax fast drying semigloss or satin varnish. You may have to touch up the varnish a second time to get the shine right. Or you could lightly sand the entire surfaces and give it a whole new fresh coat of varnish. If you don't clean and sand the surfaces first, the varnish will flake off later, so don't skip that step.
If you want them darker, you could use a tinted varnish, also known as stain/varnish in one. Minwax is a good brand for this.