In order to unlock the two Title Screen options that are blanked out at the beginning of the game, do the following:
2 player Battle Mode - Fight in an arena battle in-game
2 player Billiards - Play a game of billiards in-game
Billiards Mode Unlocks
Demon Cue - Finish Hustler King Mode
Hustler King Mode - Compete against all 14 Billiards players
Hustler Plate - Finish Tournament Mode
Tournament Mode - Compete against all 14 Billiards players
Deathmatch Mode Unlocks
Deathmatch Mode - Fight all 32 arena enemies
Deathmatch Plate - Beat all 32 enemies in a row in deathmatch mode
Skull Grill - Beat 20 enemies in a row in deathmatch mode
Support Engine - Beat 10 enemies in a row in deathmatch mode