there is buffer in printer which sends busy signal to atmega. There is buffer in atmega which sends busy signal to esp (esp doesn't have flush on uart so avr needs buffer bigger than esp hw fifo). There is buffer in esp (TCP stack). There is buffer on socket in PC. So as flow control is everywhere data caches in some buffer.

Example usage in linux(bash): echo -n -e "Hello world\r\n" > /dev/tcp/192.168.4.1/9100 

Cool, WiFi to parallel bridge. Are there any timing issues to consider? I'm not sure how much data it takes to run the printing protocol but I'd guess you need to cache most of it while you wait for the print head to catch up.