That does not appear to be a real wood top, to me it looks to be a formica-like product, as wood veneer is not usually finished to an edge like that. And the fact that the legs and vertical sides have marks in them but the top does not further leads me to that conclusion. However, I can't say for sure. Assuming it is, then you don't need to refinish the wood areas, just touch them up with a marker the same color, and spray a coat of satin of flat lacquer on them - wipe the areas down with mineral spirits first. Lightly steel wool afterwards with '0000'. Good luck.