Green’s Dictionary of Slang

1. prostitution.

1694		D’Urfey The Comical Hist. of Don Quixote Pt 2 II ii: The Girls of Venus Game, / That venture Health and Fame, / In practising Feats, / With Colds and Heats, / Make Lovers go Blind and Lame.
1724		A. Ramsay Tea-table Misc. (1733) IV 412: You girls of Venus game, That venture health and fame [...] Make lovers grow blind and lame.

2. sexual intercourse.

c.1780		‘Sally Mac Gee’ in A. Carpenter Verse in Eng. in 18C Ireland (1998) 513: You sporting young girls, give ear to my ditty / [...] / I’m a buxon young girl, just come from the city, / I love for to play at young Venus’s game.
c.1790		‘The Coughing Old Man’ in Luke Caffrey’s Gost 2: The very first night that he came to bed to me, / I longed for a trial at Venus’s game.