As is usual for these sorts of books, they choose to use a card game as one of their illustrations. The game appears to be describing a simplified version of Ruff and Trump. The discussion leaves it pretty clear that there was a lot of room for variation in the playing of the game, but it gives a good idea of what's going on. The game sounds like a particularly elemental game of luck, where the purpose is largely to wind up with the point-winning court cards.
Credit for this transcription goes partly to Anton de Stoc, who initially brought the text to my attention, and Godfrey de Shipbrook, who provided the facsimile. I've started with Anton's transcription, added a bit more before the start of the game (listing some other common games), and tweaked things back closer to the original spellings. It is possible that Anton and I are working from slightly different editions; there seem to be a couple of textual differences beyond spelling.
Note that Anton's transcription includes both a strict reconstruction based on the text, as well as a good guess of what the same game would look like as a trick-taking game.
Transcription note: there is an open question of what the "pynes" in the text are. Anton transcribed it as "pennies", which seems plausible for a gambling game. However, the book as a whole is so pious that I am nervous about that interpretation. Godfrey points out that the corresponding word in the French column is "esplingues", which is obscure but seems to translate reasonably as "pins". So I currently suspect that "pins" is the intended reading of the word, indicating that the boys are basically just playing for fun, with no money involved.
[The children are at school.]
Peter: It is almost two a clocke. Tyme to goe to play if it please you to geve us leave.
The school[master]: Children, Goe play: But take heede that you hurt not one an other.
James: I thanke you maister.
The Usher: Doe soe, that we here no compaintes on ye.
Peter: We will play quitely.
Stephen: What game shal we play at?
Peter: Let us play at dyce.
James: I did never learne to play at dyce.
Peter: Let us then play at tables.
Stephen: Our maister should not be wel pleased with all.
Peter: Shall we then play at boules?
Stephen: No: But we shall play at tanyse, or els at Cartes.
James: Let it be at Cartes, we bestow our tyme in vayne and I feare much, that our maister calles us to our bookes, before we have begon our game.
Peter: Let us then play for pynes.
Stephen: Let it be so: But let us [haste?] begin. Shall we play at Trumpe?
Stephen: How shall we play ?
Peter: The King shalbe worth six pynes. The Queene, foure: The knave, two: and eche carte one : and who has the asse shall rubbe.
Thomas: You say well: We will play my brother, and I agaynst Stephen and against you.
Peter: Will you have it so Stephen?
Thomas: Let us begin then. Who shal deale?
Peter: The same shall deale, that shall cut the fayrest carte.
James: Let us see then: Who shall deale.
Stephen: I must deale: for I did cut a kyng.
James: Deale twelve a peece.
Thomas: Nine for every man is enough.
Peter: Well deale then.
Stephen: I deale right. The trumpe is.
Peter: I rubbe: But you deale all to them.
Stephen: I can not mende it:
The cartes did rise so.
Peter: You did not shufle them wel.
Stephen: But I have.
Thomas: You doe owe me every man two pinnes, for the knave that I have.
Stephen: Let see.
Thomas: Here it is.
James: And you do owe me every man ten, for the king, and the Queene.
Peter: Show them.
James: Here be them.
all your fayre cartes, I have the game: And you do owe me every man, for six cartes.
The servaunt: Children, Come to your bookes: The schoolemaister doth tary for you in the schoole.
Peter: We doe but begyn to play. Do you call us all ready? you ieste I believe.
The servaunt: I doe not: Come I play you, least you be beaten.
Peter: Let us goe then, and we shall make an end another tyme.