Refinishing a Mersman Table?

As a general rule, Mersman tables were made of solid wood but many styles did have veneer. This table has inlaid squares so I feel sure this is veneer. They did not use anything like 'particle board'.

As to refinishing or changing color; that would have to be a personal choice and what plans he has for the table would be another choice.

Your pictures look as if the table finish is in great condition which proves we cannot tell anything about what you're relating to.

Dark flecks of stain to give it character? Not sure I understand this comment but if you plan to sell this table then I would suggest you do no more than refurbish/refinish this table as the inlaid squares are beautiful.
Some people may like a lighter finish but that would be a personal choice.
You did not ask about value so I'm assuming you do not plan to sell it but should you decide to part with it and it is cleaned up properly, you should list it with a starting price of $500 with best offer considered and local pick up or freight shipping paid by buyer.
These are the kinds of items that you sometimes have to leave listed for several weeks/months as sales may be slow. You can always lower the price if you receive no offers and wait again.
Remember; pictures sell so take good ones.