How to fix wood surface
When refinishing old surfaces like that, I have had great results finding the right compound to do what is called I think, re-amalgamation. It is when the proper solvent or compound I called it earlier, is used to melt the finish on the surface and allowed to dry again. It will remove some of the finish, or perhaps even most of it if too much is applied and wiped back off, but it requires no sanding, but you will need a respirator for the fumes. This saves the patina of the surface and will remove all the glass rings and minor scratches that was on the surface. If there are deep scratches it will not remove them, but it may color them in a bit so they are not so noticeable.

The finishes used typically are shellac and lacquer. Shellac can be removed with denatured alcohol I think, lacquer is cut with lacquer thinner.

If you really want it all clean and pristine and brand new looking, the sanding is the best way to go since the only way to get rid of deep scratches is by sanding, unless you want to try your hand at using lacquer sticks. Those are a heat melt-able filler that come in numerous colors to blend in with the color of the wood.