How are Swindler's effects resolved in a multiplayer game?
Each player reveals, trashes, and gains in turn order. The relevant text of Swindler is: 


  Each other player trashes the top card of his deck and gains a card with the same cost that you choose.


In Dominion, you do each instruction in order. The convention is that each instruction is one sentence. For Swindler, the instruction is "trash and gain." Having multiple parts of a single instruction is common in Dominion. For instance, the Bureaucrat uses the same construction. In resolving Bureaucrat, the first player must reveal a Victory card and put it on top of their deck, then the second player does both of those things, then the third.

If Swindler wanted everyone to trash, and then everyone to gain, it would have to be written as two separate sentences, and it would be a really messy wording to make sure that the cost of the gained card matches the cost of the card trashed from that player's deck.