A computing device may include a memory and a processor cooperating therewith to receive a plurality of data streams from at least one data source to be relayed to different destinations on demand, where each data stream has a respective content identifier associated therewith. The processor may further determine when a first one of the data streams for a first destination shares identical data with a second one of the data streams for a second destination based upon the respective content identifiers associated therewith, and suspend relaying the second data stream to the second destination, and begin relaying the first data stream to the second destination, based upon the determination that the first and second data streams share identical data based upon the respective content identifiers associated therewith.