As indicated in Joyce’s use of the word “game,” or some form of the like, the OED presents a variety of definitions and usages for the word. “Game,” which originates (according to etymonline.com) in its multiple forms mainly from Middle or Old English, initially served to reference a type of sport or competition, or describing one ready for that, but as these varying definitions indicate, the term takes many uses today, and in Ulysses. Definitions for “game” as provided by the OED include:

Noun:

• Amusement, sport, fun; pleasure, enjoyment, in later use only with modifying adjective, as  great (good, etc.) game.
• Jest, sport
• Freq. with the. Lovemaking; amorous sport or dalliance; (also) an instance of this. In modern (and some earlier) use often specifically denoting sexual intercourse. Now rare.
• slang. With the. Prostitution. Earliest in  lady (also girl, etc.) of the game. In later use chiefly in on the game
• Originally: a butt or object of ridicule, a laughing stock

Adjective:

• Of a person or animal: full of pluck, spirit, or fight; spirited, plucky; intrepid. Also applied to actions, attributes, etc.

• Having the necessary spirit or will for a specified challenge, adventure, novel experience, etc.; ready and willing

Verb

• intr. To amuse oneself; to play, sport, jest; (occas.) to indulge in amorous or flirtatious play. Formerly also (occas.) trans. (refl.) in same sense.
• trans. colloq. Originally: to make fun of. Later: to deceive, ‘kid’. Now chiefly U.S
• intr. To take part in an indoor game, of a kind on which stakes or wagers may be placed; esp. to play games of chance for such stakes or wagers; to gamble. Now somewhat arch