You don't actually have infinitely many moves available in analog chess since you can only click on a pixel. But while check should be doable in reasonable time

You don't actually have infinitely many moves available in analog chess since you can only click on a pixel. But while check should be doable in reasonable time, checkmate / stalemate would be expensive to compute since you have to check every possible move of yours (not just with the king, but with other pieces that could interpose as well) and then check every possible opponent's move in response to each of your moves to see if the king will be in check in the resulting positions.