In this case, "K" is 2^10 == 1024. Which is actually 57344, so the comment is wrong anyway.
This has to do with how asynchronous serial systems were designed a long time ago, with a base baud (line change) rate of 75 baud, then 300 baud, then 1200 baud etc. 57600 is 48 times 1200, so it's a common serial port speed in asynchronous serial ports. Meanwhile, once modems went above 2400 bps or so, they started to use advanced signal processing to send more than just "1" and "0" in a single line state change. up to 14400 bps, they used QAM, and over that, "trellis" coding. You can Google for "V.34" and "V.90" for more historical arcana :-)
The "56 kbps" modems were actually sending at a rate approximating 56,000 bits per second when working at full output power on clean lines, but that was actually not standards compliant and the transmission rate was limited in actuality to 53,300 bps downstream. (Upstream was typically limited to 33.6 kbps.) To drive them, you'd typically use a 57600 (or faster) baud rate on your serial port. The inclusion of 57600 may have been a confounding of the two similar speeds on the part of the original author.
That being said, those are some pretty low limits to use for games of today. Modem games do not support FPS play for 20 players. You'll want to bump up those numbers with the stated goals of your game, and require all players to have at least some kind of "broadband" connection.