Howdydiddlington! I just had a bit of a gander at Catacomb Chess And here is my feedback for you my friend!
Concept
With regards to the concept that you have acted upon here, I do find it interesting and I feel like it allows for a much more friendly way of teaching players the long term joy of that sweet table top game that is chess!
Mechanics
Now when it comes to the mechanics in this game, they do feel a tad confusing as well to be frank :S When playing with yo0ur pieces, I undrstand that you must restrict their movement to the checkerss of the board. The strange thing is though that I can pick my piece up and end the turn with it still in my hand, ready to kill a baddie :S
Aside from the above, as I mentioned the player pieces are restricted to the checkers, yet the enemies seem to be above the law of this mechanic :S As a result, this breaks away from the feeling of a chess emulation at all :S
Visuals
With regards to the art style(s?) you went with in the execution of making this game, I do find myself quite puzzled :S To start with it feeld like I am playing a game visually akin to games like Diehard Dungeon, but as soon as I get to what I assume is the levels select screen, it is like the entire artstyle changes to a more simplistic black and white stencil format (with a lot of blank space :S Maybe some form of background instead of black?)
After going through that, colour is then injected back into the visuals, though this time it doesn't feel like that first art style anymore but still the more simplistic one. I think you may need to seriously ponder and potentially redesign visuals to make it all match better on screen? :)
Audio
The audio design within this title does feel like it is nicely balanced and feels like it is appropriate for the simplistic visual style! It provides a sense of retro influence which in a way helps the player to focus more on the mechanic of chess!
Conclusion
On the whole I think that this game is a good conceptual start towards something that could be grand and played many many times and get a following! However, in ita current state it does feel rather incomplete and almost rushed in places too. I wouldn't recommend this as a profitable game...YET ;)
There ya go my good friend! Apologies for the depth but I tend to go all the way when asked for feedback, and hopefully this is all actionable! I do have a game that I am in the middle of developing right now called Shapes in the Sky. I would be curious to see what you make of the demo I released a little while ago my friend!