In a sense, this statement is difficult to justify, because Iago's plot to destroy Othello is that of an icy, jaded sociopath. But it should be remembered that he does have, in his own mind, a justification for his actions. As he says in the first scene of the play, he is aggrieved that he has been passed over for a promotion despite his skills and his apparent loyalty to the Moor. Instead, the promotion has gone to Michael Cassio, who Iago views as completely unqualified:
Preferment goes by letter and affection,
And not by old gradation, where each second
Stood heir to the first. Now, sir, be judge yourself
Whether I in any just term am affined
To love the Moor.
So Iago's entire plot, if he is to be believed (and there are those scholars who view his reasons for the plot as basically evil without motivation) is motivated by resentment over Othello's decision to promote Cassio over him. Iago's response is completely out of proportion to Othello's offense to him, and does seem to indicate someone whose obsession with revenge has consumed him. So in this sense, it could be argued that Iago has succumbed to his emotions. Iago also says at one point in the play that he suspects Othello of sleeping with Emilia, his wife:
I do suspect the lusty Moor
Hath leap'd into my seat; the thought whereof
Doth (like a poisonous mineral) gnaw my inwards;
And nothing can or shall content my soul
Till I am evened with him, wife for wife.
Here again, we can conclude that Iago is acting out of pure malice and hatred toward Othello, who he believes has cuckolded him. This would further strengthen the thesis that Iago has succumbed to his emotions. In fact, Iago's jealousy over his wife allows for an interesting parallel with the one character who is certainly governed by his emotions, i.e. Othello himself. Again, whether we believe Iago has succumbed to his emotions depends in large part on whether we accept his stated motives for his actions, and if Iago is anything, it is a skilled liar.