“equals” versus “peers” and who the rights apply to must yield to context. It is a French import of a word, thus it does not apply to lords of lower courts who are not speaking French at that time.
Look at paragraphs 52, 56, 57 and 59 and it is more clear that the barony are the ones doing the judging regarding the lands, castles, liberties, or rights. Paragraph 52 refers directly to the committee of the 25 rebel barons who were loyal to the Pope as the last resort - clearly not a dispute involving villeins and their wainnage.
Also compare par 20 and 21, where the “equal” versus “peer” context first arises in the singular case “pares suos.” A “liber homo” has no right to judgment by his equal in par. 21, while Eorls and Barons do.