If an opponent is instructed to draw a card then discard a card, and Notion Thief causes you to draw a card instead, that opponent still discards a card. The same is true of any other actions that opponent is instructed to do.

If two or more players each control a Notion Thief and a player would draw a card other than the first one in their draw step, that player chooses one of the applicable Notion Thief effects to apply. Then the player whose Notion Thief's effect was chosen repeats this process among the remaining Notion Thief effects, and so on, until there are no more possible such effects to apply. Each effect can be applied to the card draw only once this way.

The above procedure means that if each player in a two-player game controls a Notion Thief and one would draw a card, it really will be that player who draws a card.