"Word of God" here is a synecdoche for "message of God." Alternate translation: "proclaimed the message of God" (See: [[rc://en/ta/man/jit/figs-synecdoche]])
Possible meanings are that 1) there were multiple Jewish synagogues in the city of Salamis where Barnabas and Saul preached or 2) Barnabas and Saul started at the synagogue at Salamis and continued to preach in all the synagogues they found while they traveled around the Island of Cyprus.