I read through the resource the OP linked to. The authors argue the case for "AI as a new factor of production" as follows:
"But what if AI has the potential to be not just another driver of TFP, but an entirely new factor of production? How can this be? The
key is to see AI as a capital-labor hybrid. AI can replicate labor
activities at much greater scale and speed, and to even perform some
tasks beyond the capabilities of humans. Not to mention that in some
areas it has the ability to learn faster than humans, if not yet as
deeply. For example, by using virtual assistants, 1,000 legal
documents can be reviewed in a matter of days instead of taking three
people six months to complete. Similarly, AI can take the form of
physical capital such as robots and intelligent machines. And unlike
conventional capital, such as machines and buildings, it can actually
improve over time, thanks to its self-learning capabilities."
Moreover, they say that they have quantified both approaches:
"As Figure 6 shows, the first scenario is business-as-usual, assuming no AI effect. The second indicates the traditional view of AI as a TFP
enhancer where it has a limited impact on growth. The third scenario
shows what happens when AI can act as a new factor of production—there
is a transformative effect on growth."
So the critical issue here is how do they model "AI as a new factor of production" contrasted to "AI as a TFP enhancer", in order to get this dramatic difference in effects on growth.
They provide some related information in the Appendix of this white paper, for example
"We began with a modified growth model developed by Robin Hanson, professor of economics at George Mason University, Virginia, United
States. We looked at the additional increase in growth that would
occur as a result of AI by contrasting it with the baseline growth
rate. In our model, we defined labor as a continuum of tasks that can
either be performed by a human or artificial intelligence—not work
solely done by humans. The intent was to introduce intelligent systems
as an additional workforce capable of handling activities that require
an advanced level of cognitive agility."
but I would want to see much more in terms of the mechanics of economic modelling they applied.