As stated, this is too vague to be much of a hypothesis. Animals, including humans, communicate multimodally, so gesture and vocalisation are not mutually exclusive evolutionary stages. To claim that one evolved before the other, you'd need to define some relevant markers, such as grammar, cultural transmission or some anatomical adaptation.
They stated in their comment that they can never have proof and it's a bit of persuasive whimsy. This is before writing.
I find it intuitively persuasive, others may differ, but if you're going to object then keep it on vibes as we all will never have evidence.
Well I wasn't about to spend hours looking up sources and details specifying this hypothesis. All I remember now is that it's one that's taken seriously.