Which has higher priority between unsaturated ring and unsaturated chain in the nomenclature of organic compounds?
The name given by ChemDraw is: (E)-1-chloro-3-(prop-1-en-1-yloxy)cycloprop-1-ene.
The ring is determined to be the parent structure.  This is rationalised in the 2013 edition of the IUPAC Blue Book on organic nomenclature by the following rules (pg 451):

P-44.1.2.2 Systems composed of rings and chains (exclusive of linear phanes)
Two methods are recognized to name systems composed of rings and chains (exclusive of linear phanes).
(1) Within the same class, a ring or ring system has seniority over a chain. When a ring and a chain contain the same senior element, the ring is chosen as parent.  Rings and chains are chosen regardless of their degree of hydrogenation.  As a consequence, this approach prefers the choice of a ring over a chain in systems composed of cyclic and acyclic hydrocarbons
(2) The context may favor the ring or the chain, so that, for example, substituents may be treated alike or an unsaturated a cyclic structure may be recognised, or the one chosen has the greater number of skeletal atoms in the ring or in the principal chain of the acyclic structure.

So either the chain or ring may be used as the parent for the name, but the ring will define the preferred IUPAC name.
The preference of ring over chain is further clarified in the following rule (pg 596):

P-52.2.8 Selection between a ring and a chain as parent hydride
Within the same heteroatom class and for tha same number of characteristic groups cited as the principal characteristic group, a ring is always selected as the parent hydride to construct a prefered IUPAC name. In general nomenclature, a ring or a chain can be a parent hydride (see P-44.1.2.2).

All emphasis added.