"何か、機械とかに人間っぽいことをさせる、知能を持たせるみたいなまあ広い枠組みのことをAIと言って"
I think the "のこと" here is referring to/summing up everything that came before it in that sentence as what constitutes/defines this thing called an AI.
I would interpret the entire thing as
"AI is this broad term that has to do with making machines human-like, giving them intelligence and things like that."
But something closer to "verbatim" would be like
"Let's see, something like making machines human-like, giving them intelligence, well, it's a broad field, this thing called AI."
のこと doesn't really change the meaning of the sentence, and in this scenario, it broadly functions like the phrase "this sort of thing" would in English.
I don't think there is really an "exact" translation here, and there often isn't. A single Japanese phrase might even be more open to interpretation even with full context because the language itself is heavily contextual. English is linguistically a lot more precise and detail-driven, and this distinction is what makes translation so hard sometimes, which is why we use the term localization to go beyond translation toward contextualized interpretation in order to generate meaning.
I think a good approach here (and always with Japanese, for me) is to try to grasp the overall meaning first and then zoom in on the parts for the exercise if you need to, but not immediately for meaning.