Split the four instruments into two groups based on what their output actually represents. Propeller meters and Deathridge meters both work by counting rotations of a spinning element, and each rotation corresponds to a fixed volume of water, so their readout is naturally a running total, that is cumulative flow. A water meter is built for exactly this purpose too, totalling consumption over time, which is why it is used for billing.
The venturimeter sits in a different group. It relies on Bernoulli's principle, converting a measured pressure drop between the throat and the approach section into a flow rate at that particular instant. There is no built-in totalizing mechanism, it simply reports how much water is passing per second right now. To get a cumulative reading from it, you would have to integrate that rate over time with extra equipment.
Since the question asks which instrument does not measure cumulative flow, the venturimeter is the odd one out.
\[\boxed{\text{Venturimeter}}\]