Ah, I remember this when I was a child!
I still remember the floppy disk it came on, and playing it on the ol' "486" was great.
I loved the king and queen animations: my favourite was when an opposing king and queen met, and they kiss... only for an utterly brutal back-stab to occur, heh.
Another was when the rooks ate a queen.
Although there were various sequels and reimaginings/remakes, the original was pretty much the best.
I do wish someone would remake the game with better sprites: if it were an Android or iOS game, it'd be able reach a whole new generation or three, and seeing a queen get devoured by a rook on some guy's phone on the train would be hilarious.