wooden floor chipped from PC Case
What came off is the finish (urethane, polyurethane, or varnish), not the wood.

If left alone, it will absorb dirt, moisture and darken.

I would try a wipe on polyurethane and apply it with a q-tip. Your finish looks like gloss, so I would try that level of sheen. You can always dull it a bit with fine steel wool.

You should try to remove the rubber stain first. That can be done with a cleaner, such as Simple Green or Fantastik type cleaners.