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I think the title in English is not a perfect translation of the Japanese title. For one thing, the "fire" (炎) refers to Sakata, not the games, and shoubushi (勝負師) in everyday Japanese means gambler. I think it could mean competitor here, or something like that, so a more accurate title might be "Firey Competitor-- the games of Sakata Eio".
Note that the "fire" character is omitted in the Taiwanese edition.
Yes, the translation is poor. The gambler is Sakata, and flame modifies gambler.
Not that I have a translation of which I am confident. The phrase, "plays with fire" comes to mind, but I do not know if there is a similar idiom in Japanese.
Or perhaps there is a metaphor like, "gambler on fire".
Or perhaps flame modifies game (shobu), which would yield, "Master of fiery games: Sakata Eio". The title could even be ambiguous. (The Japanese like word play.)
Anyway, my Japanese is good enough to see that the translation is bad, but not good enough to offer a good one.