In order to collect royalties you must own the underlying property. This would apply to music which is owned by one of the music publishing companies set up upon the sale of MGP. Everyone else gets residual payments. Anyone who belonged to a union which provides for residual payments, such as AFTRA (the talent guild) or the Directors' Guild, would receive residuals.
Brett and the other regular panelists on MG were under personal services contracts which may have granted them nothing in terms of residuals (in the '70s no one thought game shows had any rerun value) in exchange for being paid $250,000 per year. Johnny Olson's estate may receive residuals as he was merely a daily-hire worker. The other panelists not under contract to G-T (e.g. Betty White) may receive residuals for their appearances on MG. Betty presumably also receives residuals not only for her own appearances on Password and Password Plus, but if she is an heiress to Allen Ludden's estate, receives residual payments for his appearances on P and P+. I don't know about Gene Rayburn's deal, but I do know that a certain talent agent negotiated substantial increases in residuals for emcees (at the behest of Ann Cullen) when GSN started up.
The other person who stands to receive residuals from game show reruns is the director. If their Directors' Guild contracts applied to cable, Paul Alter and Marc Breslow still have an income stream from all of the shows they directed over the years which are rerun on GSN.
Everyone else gets zero in the way of residuals, including producers and non-Guild writers. Ira Skutch gets zero for each episode of MG rerun on GSN, but gets a payment for each episode of Blockbusters he directed. The payment is only for directing, not for being E.P.
So yes, presumably Tom Kennedy and Jamie Farr receive residuals for their appearances.