What does it mean to “die game”?

Here is the entire sentence from the English translation on Wikisource:

During this time, the farewell ceremony was taking place. I have already said that this magnificent function was being given on the occasion of the retirement of M. Debienne and M. Poligny, who had determined to "die game," as we say nowadays.

Here is the corresponding part in the French version (on Wikisource):

Pendant ce temps avait lieu la cérémonie des adieux.

J’ai dit que cette fête magnifique avait été donnée, à l’occasion de leur départ de l’Opéra, par MM. Debienne et Poligny qui avaient voulu mourir comme nous disons aujourd’hui : en beauté.

One can translate "mourir en beauté" (literally "die in beauty") as "to end on a high note". (Gareth Rees mentioned in a comment that "game" here means gamely.)

In spite of the fact that Debienne and Poligny are retiring as opera managers,

Everybody remarked that the retiring managers looked cheerful, as is the Paris way. None will ever be a true Parisian who has not learned to wear a mask of gaiety over his sorrows and one of sadness, boredom or indifference over his inward joy.