Bond angle is largely governed by the location of electron cloud with regard to atoms in a molecule.
In dichlorine monoxide, the electron cloud is more spread out between oxygen and chlorine while in the water molecule it’s much closer to the oxygen atom. Therefore, the net bond paid-bond pair repulsion is higher in dichlorine monoxide than in water, while the lone pair-lone pair repulsion is almost the same.
Also, chlorine atoms are much bigger than hydrogen atoms, because of which they also undergo steric repulsion causing the bond angle to further increase.
That’s why the bond angle in dichlorine monoxide is greater than in the water molecule.