The chess scene shows Alonso both that his beloved son Ferdinand is not dead and that his son is playing chess with a woman he is clearly in love with, Miranda. Miranda also reveals herself to be in love with Ferdinand, saying, in effect, that no matter what strategic, chess-like moves he might make in real life, she will support him:
Yes, for a score of kingdoms you should wrangle,
And I would call it fair play.
Alonso is delighted that his son is alive, and Alonso is accepting of the relationship between Ferdinand and Miranda, though he says he will lose his son a second time, presumably to marriage.
The chess scene is significant for revealing good news to Alonso. It is also significant as the first time Miranda sees a whole group of men. She is excited by the sight, saying:
How many goodly creatures are there here!
(The entire section contains 2 answers and 460 words.)