afk

Urbandictionary is full of definitions for this word that say it means "away from keyboard" (in gaming), i.e. the player is inactive, doesn't respond to greetings, such and such. Most of the time, this is what it means.

I would like to give a specific example to further flesh out its meaning: in RuneScape, there is such a thing as "afk training". Literally it's a playing style where you are not literally away from the keyboard or even inactive, you're just doing something on a split screen or paying little attention to what's going on in the game itself as you train your skills, because they are designed to be done "afk", or more accurately, "semi-afk". We just call it afk in this game no matter what.

player1234 is afk... he hasn't been responding to my messages for at least 15 minutes (general example)

rang3r4lyfe is training his firemaking in the most afk way possible, burning protean logs (RuneScape-specific example)