Library or Tournament Size Jaques Set?

It looks great Minarima, I think it was a good choice - after all you want to use the board, it's not like it once belonged to Henry VIII and hasn't been touched since. Presumably the finish that was re-applied was French Polish - i.e. shellac - exactly the same stuff as the original finish, and applied in the same way.  

The board looks much better after restoration.  It's the same antique board without the discolored yellow shellac.  No way you did any harm to its value by restoring it.  

Refinishing an antique does not normally increase its value.....in fact, for a true antique, it's generally just the opposite...

However, in your case, since you say the only thing done was to carefully remove the old French polish and apply a new coat, you may be able to get away with it, without affecting the value.

On the other hand, if your primary motivation is to enjoy the board, then I wish you much happiness using it!

The image above is an antique french mahogany chest of drawers circa 1810.  You think it has not been restored?  The price is $20,000!

Google "valuable antique furniture", and you will see beautiful pieces in perfect condition and flawless finishes.  Leaving antiques  with their aged finish, scratches, fading, discoloration,  and cumulative damage does not do justice to the beauty of of the piece.  

https://www.thesprucecrafts.com/ways-to-ruin-antiques-148892

It's a strange one - you should never touch an antique gun (according to "Pawn Stars"), not even clean it - whereas (on "American Restoration") anything coca-cola related gets blasted back to bare metal and repainted

The furniture people on Antiques Roadshow are adamant: Never touch the finish (leave it to the pros to determine what if anything is to be done).

French polish (basically shellac) is a fragile and repairable finish.  Most things of 100 or more years age are already damaged to some degree.  What reduces the value of things is modern finishes, non-reversible and unsympathetically applied that make the refinishing obvious.  An intact finish on a piece of furniture has a role in preserving it, slowing down moisture changes and protecting the surface to some degree, veneer in particular is better off sealed from the air.  If you've got something that is perfect, sure, refinishing it will reduce its value, but most furniture is not that perfect and needs some work.  Over repairing, the American Restoration syndrome, leads to implausibly polished, more or less remanufactured, items that might as well be new.  For guns, the alternative example, intact gun blue should be left strictly alone, but a valuable gun with patches of ferric oxide (red rust) among the blue however is going to be re-finished regardless because the finish is damaged and not protecting the metal.  Now, did that board really need refinishing?  No idea.

In other words you can touch the finish.  You just have to know what you are doing.

Just broad generalities in that article.  This may be ok but that may be bad etc.

Yes, I think that's a fair way to put it.

I was led to believe by my restorer that French polish is actually a process/ technique, rather than an actual substance? but to answer your question yes it had the same form of polish reapplied as it would have had originally back in the 19th century.

So which generality recommends refinishing an antique to increase its value?...

The article says that its not always best to refinish, and that cleaning may be done improperly.  It certainly does not not say that refinishing is automatically bad.  Look at high end valuable antique furniture as I posted above.  Very expensive and beautiful pieces, almost always refurbished, carefully, correctly, properly.  

Where is your proof of this assertion?

Old stuff that is in such poor condition as to have little value in its current condition, and/or items for which there is little market demand might have their value increased by refinishing.

However, antiques which are rare and in significant market demand will be unlikely to have their value increased by refinishing.  That is the reason for the general consensus of those who understand the antiques market that antiques which currently possess significant intrinsic value and demand not be refinished.

Yes that's right - it's the technique of applying shellac dissolved in ethanol, building it up in many layers to get the desired finish.

Sorry if my wording was a bit crap!