"In general equilibrium analysis, agents do not interact with one another directly, but only through impersonal markets. By contrast, in game theory all players interact with all other players, with outcomes specified by the game's payoff matrix."
Brian Arthur et al aren't so much contrasting game theory against GE analysis here, although that is what it sounds like. Rather they are saying that GE and GT have something in common, and they propose a model of economics, "complexity," that moves away from that commonality.
The quote comes from a introduction to a volume published in 1997 by the Santé Fe Institute, and as Arthur later wrote it was "as close as out economics program ... came to a manifesto."
The commonality is that interaction structures in both of the older theories are simple and extreme, either one-with-all or all-with-all. In complexity, agents are chunked, so some interact more with their neighbors than with distant parties, and interact with distant parties only indirectly through the chunking.
That, BTW, is Brian Arthur's photo above.