The "bot" in gamebot certainly is meant to convey a robotic nature, in other words a one-track mind perhaps lacking in human emotions. If we can agree on that, what do we then mean with the prefix "game"? I think that the gamebot sees everything as game: their human opponents as game pieces and their human interactions as game moves. Altogether, not a flattering term.
Probably in an effort to demonstrate they "get" that Survivor is also an emotional and human game, fans tend to employ the word liberally, directing it at virtually anyone at all who is perceived as nerdy or strategic, even though being a strategic player doesn't preclude one from understanding and engaging in the social components of the game whatsoever.
In fact, one could argue that calling someone a gamebot is itself interpreting a fully three-dimensional person, as we all are, in a two-dimensional perspective, and therefore is hypocritical and reductive. All in all, it's fairly useless as a term, especially with how widely the label is used, and people should just say "very strategic," "less charismatic," "less social," and so on.
