God this is such a cool concept and it works incredibly well. I always toyed with what would need ot be done to have a sense of "party" with relationships and make them impact gameplay, and this is such a good implementation of that.
The idea is amazing. The mesh with chess is interesting, but I don't think it's what makes the game. It could be classes particular to this game instad than ches spieces and not much would be lost, maybe even gained (The queens felt so OP compared ot the pawns, and having just one move each turn incentivises not using weak units at all. Maybe you should be able to move multiple units in a turn)
I also toyed a lot with a concept for a game similar to maybe hearthstone, but instead of building a deck you build a board and with your prebuilt board you fight other players. Maybe that's the direction this could take.
I don't know, I'm just rambling. This concet really inspired me, I hope this grows. I'm sure I'll steal some design ideas for some projects of mine in the future.
If you need any help, apart from the highest praise I can give, just tell me, I'd be delighted to help.