Define a grammar to emmulate chess rules
"The way chess apps work(not engines), is that at every move they calculate all possible moves and then check if the user's move is among the calculated moves, else it is invalid."

No, no, no, no, that's not how you check if a move is valid. 

If you want all possible moves, then you generate all possible moves. If you want to check if a move is valid, then you check if that move is valid, and nothing else. There's no reason to know anything about all the other moves if all you want to know is to check if one move is valid.