Protest?

[Dakota]

Taking the play by the book & ignoring the umpire's call of "BALL GAME" is an umpire not facing the music for his mistake, IMO.

True, the players are in jeopardy of being appealed out if they do not complete the circuit of the bases (ASA 8-3-I).

However, the umpire in the situation described needs to consider if his erroneous call of "BALL GAME" placed the runners in jeopardy - i.e. whether they would have completed the circuit of the bases were it not for his call. To me, it appears that he did place the runners in jeopardy with an erroneous call and he must rectify that.