Quadrille, as named in the last line of the poem, is the game. (This web page has lots of details and further references.)
I don't know exactly what "known shuffle" means here. "Sword" seems to mean "spadille", the ace of spades. I assume Cosmo is the name of one of the players.
Check out, eg, A Brief and Necessary Supplement to All Former Treatises on Quadrille: Consisting of Hints, Questions, Explanations, References, Suppositions, &c. for the Benefit of the Unlearned by "No Adept", of
1764. (See this online copy.)
An excerpt (with modernized capitalization) from page 3:
Wherefore, without further introduction, as the difference between a Sans prendre and a Vole, seems not sufficiently attended to by young players, I shall begin with the following illustration of it.
Suppose, for instance, two fish on the board, and eight remaining in the pool, a Sans prendre without matadores is one fish better than a vole without matadores : and with matadores, it is two fish better than a vole with matadores. Without matadores it is a matadore better than a vole with matadores and with matadores two fish and a half better than a vole without matadores.
I can almost imagine Moody writing with "No Adept's" handbook open in front of her.