What is required for a starting player to re-enter the game without penalty?

The correct choice highlights a specific rule regarding player re-entry in a game setting. When a starting player is substituted, they may return to the game to face a specific requirement: they must pitch to the first batter after re-entering. This rule ensures that the integrity of the game is preserved by requiring the re-entering player to engage in play immediately, which adds consistency and accountability to the substitution process.

The other options relate to additional rules about player participation, but they do not apply to the specific requirement for re-entry without penalty. For instance, while waiting until the next inning or limitations on additional substitutions may be relevant in different contexts, they do not pertain to the direct act of re-entering the game. Additionally, the rule about batting in the original order applies to lineup consistency, but it does not directly pertain to the conditions under which a player can re-enter the game. The emphasis on a player facing the first batter upon re-entry acts as a check and ensures that players can contribute to gameplay in a structured manner.