A question involving immunoprecipitation to identify interacting proteins?
First: You are right with your reasoning that Protein X (X) and Dcr-2 interact directly. Lets go through the blots: In the input you check for the proteins loaded into the setting and stain unspecifically with Coomassie.
This part of the blot shows you no unspecific input, and both proteins of interest present. This also shows that Dcr-2 is much bigger than X which allows an easy identification of band patterns.

In the eluate you will only see proteins which are bound directly in the reaction or which interact with bound proteins. Dcr-2 is Flag-tagged so it will directly bind to the beads and can be eluated from them. This is shown in the coomassie part of the blot. Dcr-2 alone binds and can be eluated, while X alone does not bind and therefore gives no signal. Dcr-2 and X together give two bands, sind Dcr-2 binds to the beads and X is interacting with Dcr-2.

This binding is also shown with the anti-His antibody which only recognizes Protein X. The protein shows up in the input where X is added. It also shows up in the elution lane (where Dcr-2 is also present) showing that X is an interaction partner for Dcr-2.