Cluny Macpherson was a real-life Highland chief of the clan of Vourich (or Vurich). He fought for the Jacobites in 1745 then managed to stick around Scotland without being captured for ten years before leaving for France. Cluny gives Davie and Alan shelter in Chapters 22 and 23 (a lucky thing because Davie falls ill), but he's also the cause of the worst quarrel between our two main guys.
Cluny draws Alan into a game of cards. While Davie lies in bed sick with fever, Alan borrows some money off him, which he then promptly loses to Cluny. When Davie comes to, he realizes what Alan has done and basically guilt-trips Cluny into giving him back his money. But Davie's still furious at Alan, who now has no money to contribute to their travels, for taking advantage of him while he was sick. Not cool!
Cluny's role in the book – beyond this plot-advancing function – is to provide yet another example of the differences between Lowland and Highland values. Davie's Puritan upbringing has taught him that cards are immoral, which leads Cluny to ask: "What kind of Whiggish, canting talk is this for the house of Cluny Macpherson?" (23.21).
The thing about Scottish politics during this period is that everything is connected – religion, politics, family, everything. So if you're a Highlander, that also implies that you (a) might be Catholic, (b) are probably faithful to a clan, and (c) are possibly a Jacobite. If you're a Lowlander, that suggests that you (a) may be a Whig (a supporter of the current king of England) and (b) are probably a Protestant (either a member of the Church of England or the Scottish Presbyterian Church). So if you're wondering what the heck Davie speaking out against gambling has to do with his political support for the king (i.e., his "Whiggish" talk), this is why. Being a Whig and being a (puritanical) Protestant both go hand in hand with Davie's identity as a Lowlander.