Why does Shakespeare include this plot event? to establish Claudius's respect for Laertes to illustrate Claudius's skills of manipulation to showcase Claudius's wartime experience to present Claudius's interest in competition

To illustrate Claudius’s skills of manipulation

Shakespeare include the plot event in the act IV of Hamlet in which Horatio reads and reacts to Hamlet's letter about an encounter with pirates because of the reason to establish Horatio's steadfast loyalty to Hamlet. The answer in this question is establish Horatio's steadfast loyalty to Hamlet.