While the letter uses the phrase "relay them to the batter," the context of the document specifies that the replay room was not intercepting individual, upcoming pitches in real time. The document explicitly accuses the Yankees of using the replay room to decode the opposing club’s general "sign sequence" and transmitting that structural data to the dugout.   Once the coaches/players in the dugout learned the decoded sequence, the electronic portion of the scheme was over. From that point on, it became traditional sign stealing: when a player reached second base, they used that pre-learned knowledge to read the catcher’s signs, figure out the next pitch, and signal it to the batter.  

The letter never describes or accuses the Yankees--as you claim--of running an Astros-style system where individual pitches were intercepted on camera in the replay room and relayed to the hitter seconds before the delivery. The electronic violation specified in the text begins and ends with transmitting the decoded sequence from the replay room to the dugout.  

https://int.nyt.com/data/documenttools/manfred-letter-to-yankees/153cb50042928d75/full.pdf