As you know, the first box on the right must be white. By default the table does not rotate, which produces an inconsistency that we will now solve.

The idea is to modify a word in a file. The file is called Buildings_Joy
The path of that file on my PC is:

C:\ProgramFiles(x86)\Steam\steamapps\common\RimWorld\Data\Core\Defs\ThingDefs_Buildings\Buildings_Joy

Once the file is found, we open it with Notepad, and look for the following text extract:

<ThingDef ParentName="FurnitureWithQualityBase">
<defName>ChessTable</defName>
<label>chess table</label>
<description>The ancient game of kings. Fun for a few hours here and there, even playing alone. It trains intellectual skills.\n\nThis building requires adjacent chairs or stools to use.</description>
<graphicData>
<texPath>Things/Building/Joy/ChessTable</texPath>
<graphicClass>Graphic_Single</graphicClass>
<shadowData>
<volume>(0.65, 0.25, 0.6)</volume>
<offset>(0, 0, -0.15)</offset>
</shadowData>
<damageData>
<rect>(0.09375,0.296875,0.796875,0.703125)</rect>
<cornerTL>Damage/Corner</cornerTL>
<cornerTR>Damage/Corner</cornerTR>
<cornerBL>Damage/Corner</cornerBL>
<cornerBR>Damage/Corner</cornerBR>
</damageData>
</graphicData>
<altitudeLayer>Building</altitudeLayer>
<rotatable>false</rotatable>

In the <rotatable> section we replace the word "false" with "true". We save the file, and that's it. The chess table can be rotated like any other object.

NOTE: The "BIOTECH" update restored the files. If you changed them before the update, change them again.

Ideally, Ludeon Studios would release a patch, since visually it's not perfect.
Thanks to @Ninefinger for the solution.