In a Commander game, if you poison out one opponent do the other opponents continue playing?

In any multiplayer game of Magic, each player's life total, poison counters, and loss conditions are tracked independently. A player loses the game when they meet a loss condition — such as having 10 or more poison counters — but this only eliminates that specific player. The remaining players continue the game normally (CR 800.4a, 104.3c).

Commander uses the "last player standing" format by default, meaning the game continues until only one player remains. Eliminating one opponent through poison is a valid path to victory, but the other opponents stay in the game and keep playing (CR 810.2).

It's worth noting that in Commander, the format-specific rule of 21 commander damage also applies only to the individual player receiving that damage — another example of how all combat damage, poison, and life loss are tracked per-player, not globally (CR 903.10a).

Example: In a 4-player Commander game, you use an infect strategy to give Player A their 10th poison counter. Player A is eliminated immediately. Players B and C are completely unaffected — they have their own poison counters (likely 0), life totals, and board states, and the game continues among the three remaining players.

So yes, poisoning out one opponent is simply one elimination in a multiplayer game. The others keep playing until only one player remains and wins.