Why is the received signal=information+RF signal+noise,not just information+noise?
Well, it seems the authors assume a setup where there are separate data receivers (DR) and energy receivers (ER) ("To achieve a balanced user experience for separately located datareceivers (DRs) and energy receivers (ERs) in the network, joint transmit beamforming vectors are optimized [...]"). In that setup, $s_k^E$ would be symbols that are used for sending energy to the ERs whereas $s_k^D$ are data symbols for the DRs.

Therefore, if you are a DR and want to receive data, you care about two types of interferences: data symbols for other DRs and energy symbols for the ERs. Note that you didn't copy equation (1) exactly: the second term should be $s_i^D$ (data symbol interference). Then you have the third term with interference of energy symbols for the ERs and the fourth term for the noise.

As an ER, you wouldn't care about interference, it's actually additional power, if you like.

Other papers use other models where one node may want to receive data and harvest energy at the same time. As they say: "all models are wrong, but some are useful..."