Although you can certainly read it that way, I don't think that was his intention. From the broader context, I believe he was trying to use it clinically and not as a derisive insult. He was trying to understand the mechanisms which made people have emotional connections with a computer program.

"Maybe it's because people saw it as a tool and people become emotionally attached to tools" you may think. Coincidentally his chapter following that is entitled "On Tools" where he goes into psychological literature on human-tool interaction.

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Also there's an unspoken context here that he gets a step away from a few times without hitting it:

Non-technical people understood computers from their popular depictions; perfect electronic brains; profoundly superior-to-human machines.

Some people likely assumed there was an infallibility to the interaction, as if someone, say unfamiliar with stage magic, saw a magic trick and assumed it was sorcery. People employ whatever mental model they're familiar with that fits best.

The idea it was merely just rearranging your words and feeding it back at you likely seemed just outrageously galling to be the thing a multi-million dollar machine that takes up an entire room and coming from the MIT Artificial Intelligence Lab is doing. No. It must be real...

Almost as outrageous as someone suggesting your sorcerer simply put the item in his pocket while he was distracting you.

Eliza, in 1965 was a computer version of Uri Geller.

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Another idea relating to Milgram, he never pointed out whether people trusted that a machine would have had safety precautions built in. Of all his variations I'm not familiar with any where he made the machine "malfunction".

Would subjects then trust the proctor but distrust the machine and back off more or perhaps, even more interesting, would there be no difference at all?

If someone made a version of Eliza for victim culture, "the bit about [message subject] is incredibly condescending" could be one of its stock phrases.