In the context, emotional intelligence serves us, is useful, helps and benefits us rather than makes us into slaves, dictates what we do, forces us to do things.
It looks like a woolly psychobabble to me, in all honesty, as such a statement can be applied to any cognitive skill/ability. I can't think of a mental ability or competence that enslaves people. But that's probably beyond the scope of the forum.
I'm not conversant on "emotional intelligence," but wikipedia speaks of evaluating and managing one's emotions and those of others.
I suppose that managing one's emotions could be considered a stricture, binding or enslaving our true natures under a mantle of pragmatism or civility. The writer is suggesting that this is a tool rather than a burden. It will help, not hinder.
The writer could mean a kind of intelligence that springs from the emotions, rather than "managing emotions intelligently". Emotions might be said to enslave us, since they are to a great extent out of our control and can perhaps make us do things we would not otherwise consider sensible. However this intelligence that derives from emotions tends to serve rather than enslave. I don't endorse this theory in any way, but it strikes me as a possible meaning.