Very solid base for a tower defense, now's the time to figure out what direction you want to go in! I checked out a bunch of other TD games recently, from older flash games as well as newer games too and I noticed all of the best ones have some kind of unique mechanic or structure to the game. Whether you can upgrade the towers, combine them together, directly attack the enemies coming in, multiple paths, etc. I think Chess TD needs that hook that can pull people in, because this currently isn't any more complicated than something like Desktop Tower Defense from like 2007, and even that game had the unique premise that you could build a path for the enemies to take with the towers themselves, potentially creating a maze for them so you can land more hits on them. Sometimes less is more, but I don't think that applies here unfortunately.
The game's balance doesn't feel quite right: you lose exactly one health point no matter the strength of the enemy pieces that get through, and you only get 5 chances, so instead you could lets say 100 health, and you take the heath/strength of the peices that make it through and subtract that away from the player's health to better balance the health. Maybe it could recharge by 5 each round won? The Rooks and Knights feel way stronger than the pawns, so maybe they could be nerfed. You'll also need more variety in the towers, 3 towers that shoot the same kind of projectile at different rates and different ways just doesn't seem like enough. You could add special towers that slow them down or give them poison damage, maybe one that makes it so when a piece is defeated it creates a damage radius, great for areas with high volumes of pieces.
I think once you figure out what additional mechanics and specialties (beyond a Chess theme that comes with some minor enemy variety) your game has to offer, it'll boost the game's quality by a long shot! But, it'll only go as far as you'd be willing to take it. I'd research what other TD games have tried before to help brainstorm ideas, so your game doesn't get checkmated by more complicated and exciting TD titles. Looking forward to seeing this one develop!