I am currently in a theme league that uses a non-standard schedule. The schedule includes a few cycles where my team does not have a game. Do my players rest or recover from fatigue during this cycle without a game?

No - players do not recover fatigue or rest during this cycle without a game. Some of the non-standard schedules require some cycles where a team or two do not play a game. This is to accommodate the balanced matchup of teams over a full-season. As a result, teams do not rest during this cycle or else it would provide the team/players an advantage. Players only receive rest from non-game days during the all-star break and each round of the playoffs (if they defeat their team in fewer games than their next round opponent).