Does this quote from the TV show Devs confuse chaos theory with quantum theory? In the dam scene in Episode 7 of Devs, one of the characters says:

A few moments from now, you climb over this rail, you stand on the other side and balance there, right on the edge of the dam. Just your toes on the concrete, arms outstretched not holding the rail. Whether you stay balanced or fall depends on quantum variations of the air around you, the wind. If you believe in [the many worlds theory] there will be worlds in which you fall, and worlds in which you don’t. 

My understanding is that wind and weather are difficult to predict due to being a chaotic system, however they could be deterministic given enough time/computational power, measurement accuracy.
Is the writer confusing the probability of falling given some inexact initial state with “quantum variations”?
 A: Hard to see how either quantum or chaos theory are involved. The person standing on the edge of a platform is analogous to balancing a pen on its tip. The body is unstable and sensitively depends on its initial position and surrounding factors. Sensitivity alone isn't enough to imply chaos. 
A: Let’s first start with what we get from quantum and chaos theory that affects the situation in question:


*

*In most interpretations of quantum theory (including many worlds), events on the particle scale are subject to randomness. This can be experimentally confirmed for some constraints on randomness (without those, you cannot prove or disprove whether the universe is deterministic or stochastic).
In fact, if we extrapolate this aspect of quantum theory to big scales, everything is subject to randomness, but the probabilities for somebody standing on a dam being shifted 1 cm all of a sudden become excessively small. Therefore it is safe to ignore this in application and this cannot be experimentally tested.

*Chaos is a property of deterministic model systems. Such systems are subject to the butterfly effect: Tiny changes of the system will eventually blow up. When ignoring quantum effects, any sufficiently realistic model of reality is chaotic.
If we combine the two, we get that quantum randomness on the particle scale will eventually blow up to cause big changes. Specifically, details of the collision of two air molecules can determine whether a storm happens a few months later.

My understanding is that wind and weather are difficult to predict due to being a chaotic system, however they could be deterministic given enough time/computational power, measurement accuracy.

A detailed model of wind and weather that stops at the particle scale could be deterministic. But in reality, it doesn’t stop there and thus real wind and weather aren’t deterministic (when you assume quantum randomness as given).

Whether you stay balanced or fall depends on quantum variations of the air around you, the wind. If you believe in [the many worlds theory] there will be worlds in which you fall, and worlds in which you don’t.

Let’s assume that whether you fall is primarily determined by the details of wind gusts.
These are part of a chaotic system and thus inevitably decided per quantum randomness on the particle scale.
However, since the butterfly effect takes some time to build up from the particle to the human scale, it is not quantum randomness currently occurring in the air around “you” right now, but the one occurring considerably earlier.
So the two kinds of worlds mostly branched off much earlier than now and you are already in one of these worlds, you just cannot tell which one.
Apart from that last detail, I have no objection to this statement.
A: I think  "quantum variations of the air around you"  is the confusing part. It is not just quantum variations  of the air, your body plays a big role.
As (in mainstream physics) all forces in nature are emergent from the quantum mechanical framework, to attribute everything to quantum variations would be OK, as happens with the many worlds interpretation , which takes a specific mathematical framework of quantum mechanics literally. It is just the "air" that makes it an inadequate statement.
