Considering that we don't have any history of chess until more than 500 years after Seneca's death, in India no less, I think it's fair to say that this is yet another example of "ye olde translationes" editorializing and using too much dynamic equivalence. latrunculi, the word he uses in this sentence at the beginning of chapter XIII, must have referred to a different game.

Plus, I doubt most people would really agree with de brevitate vitae. It's the equivalent of "grind culture" but from the first century. Amusing and interesting but probably not congruent with now most people want to spend their lives. (No shame from me if you do want to live your life that way, but it should just be known that this is far from a neutral perspective.) For a more balanced view of otium (pleasure, relaxation, opposite of negotium, business), I'd recommend the letters of Pliny the Younger.