The word "engendered" can have many meanings. Here there are two main interpretations of the word.
First, the word most obviously entails conception via sexual intercourse, which is certainly true in Leda's case. The word can be used to refer to both the male and the female, but the "shudder in the loins" (though deliberately unclear) seems more to refer to the swan than to Leda.
Second, the word can be used as a metaphor any sort of inception or beginning. Here, this, too, is true, but more subtly. Yeats uses both these interpretations equally to link this violent sexuality with destruction and death that culminates in the modern age. When combined with the above definition, this destruction and violence is the fault of the swan, not of Leda, but it is Leda who must bear the responsibility and weight of this act, and bear these children who will instigate the War.