That's consistent with the following modified claim: in the absence of firm knowledge of how agenty a thing "really" is, you will tend to take its unpredictability as an indication of agentiness.

I think unpredictability is a complete red herring here. What I notice about the original examples is that the perceived lack of agency was not merely because the game-player was predictable, but because they were predictably wrong. Had they been predictably right, in the sense that the expert player watching them had a sense of understanding from their play how they were thinking, and judging their strategy favourably, I doubt the expert would be saying they were "playing like a robot".

I happen to have a simulation of a robot here. (Warning: it's a Java applet, so if you really want to run it you may have to jump through security hoops to convince your machine to do so.) In hunting mode, it predictably finds and eats the virtual food particles. I am quite willing to say it has agency, even though I wrote it and know exactly how it works. A limited agency, to be sure, compared with humans, but the same sort of thing.