his wife whose sister was elected as a city delegate を　
How excited the student was !　のthe student の部分に代入すると、本来なら

How excited his wife whose sister was elected as a city delegate was!

となりますが、この場合 How excited と was の間隔が空きすぎて
意味がすっきりしないので、his wife の直後に was を移動させた表現です。

How excited his wife was, whose sister was elected as a city delegate !

このように語数が多い場合、語順を変えるケースはたくさんあります。