I'm actually okay with the dark BG in shot 1 and like others have said - nice and sharp and good comp. For me this is a case where off camera flash would have worked very well to light the chess pieces which I find dark.

Shot 2 is a stronger image imo based on comp and lighting, but I agree that blurry bishop in the midground is a distraction. For this particular shot It would likely have been best to focus just beyond the blurry bishop.