Don´t know how chess has something to do with this map, because I didn´t encounter anything that could have related to chess, but anyway, it was a mediocre map. Detail, layout, design, texturing, lighting... all on beginner´s level from year 1996. The only good thing was bugfree design and very low amount of misalignments. OK, I don´t want to be rude, but this is quite bad map, but still minor improvement since Strip Hotel. Too complex and cramped areas are gone, but map has still much to forgive. You should try to create interesting layouts like symmetric shape to your map and many different routes to same places. It makes the gameplay more interesting.
To improve your lighting, I try to demonstrate how big gap there is between lighted and non-lighted box. Lighting creates the shape of the object and in Duke Nukem 3D, it makes environments look more interesting and realistic. Good lighting saves a lot, so try to put more effort into it. Also you could try to create trimwork using pillars with good lighting. It also makes map´s look better.
Two pictures, guess which one doesn´t have any lighting at all. I bet you can see the difference:
