Round-robin games have been around a long time. Basically, all it means is that various people in the gaming group take turns running the game. The main decisions in this type of game are how to handle the rotation between gamemasters, whether the current gamemaster has their character along as an NPC.or has the character off doing something else, and whether the gamemaster's character gets credit (usually in the form of experience points) for the adventure.
This style of play has a few interesting effects in The One Ring. If a character is absent for some adventures, they spend less Hope, but still have the opportunity to recover Hope during a Fellowship phase. Likewise, if they miss an adventure, they haven't gained Shadow points during that adventure (though, they also won't remove Shadow during the Fellowship phase if they didn't take action that interferes with the return of the Shadow. These effects may make certain characters more attractive to a round-robin Loremaster (Rangers, Elves, and High Elves). This can be especially attractive when the characters are only undertaking a few adventures per year...which means a greater portion of Fellowship Phases occur at Yule.
Granting experience is another factor that has to be considered. If you give the characters of round-robin Loremasters the skill and adventure points they would have gotten as a player, then the character has gained something without being part of the adventuring group. However, if you don't, those characters will fall farther and farther behind the rest of the group over time, which will affect their ability to equally contribute. Regardless, being the Loremaster means your character doesn't get the material rewards, including magical treasures.
Finally, adventuring can be deadly. If a Loremaster runs their character as an NPC during an adventure (which may be necessary if the group is short on players), are they equally at risk, and if so is it a satisfying outcome for your character to die when you are running the game?