Does Notion Thief replace draw effects that say 'that player draws' during a multiplayer free-for-all?

Notion Thief has a replacement effect (CR 614.1) that modifies any event where an opponent would draw a card: instead, that player skips the draw and you draw a card. This applies regardless of how the draw was triggered — whether from a spell, an ability, or an effect that says 'that player draws.'

In a multiplayer free-for-all, 'opponent' means any player who is your opponent (CR 102.4), which is every other player at the table. So Notion Thief intercepts draws from all of them simultaneously if multiple players are affected by the same effect.

The phrase 'that player draws' is simply shorthand for a draw event targeting a specific player. Per CR 120.1, any time a player would draw a card by any means, replacement effects that modify draws — like Notion Thief's — apply to that event. There is no special exception for indirect or targeted draw phrasing.

Example: You control Notion Thief in a 4-player game. An opponent casts Howling Mine's trigger causing each other player to draw a card. Both of your other opponents would draw — instead, you draw two cards (one for each opponent), and those opponents draw nothing.

Note: If two Notion Thieves are on the battlefield controlled by different players, the draw replacement layers can interact; the player whose turn it is (or the player who would draw) chooses the order of applicable replacement effects per CR 616.1.