What does it mean that a substance can be smelled from far away?
You are not missing anything. Rather I think you are placing too much emphasis on the scientific accuracy of something said for effect in a very chatty presentation.
The spoken words almost instantly are not repeated in the headlines, whereas the rest of the quote is. And the presenter does not develop this idea of being able to smell thioacetone almost instantly, so I doubt that he is making a scientific claim that it diffuses extraordinarily fast. What is being emphasized is the distance - which equates to being able to detect the chemical at very low concentrations.
The wikipedia article on thioacetone cites the experience of Esso researchers in 1967, who detected the chemical "downwind within seconds" from about $400$m away. It is not stated how many seconds, nor the wind speed. Since the average speed of air molecules is around 500 m/s, the transport of thioacetone by $400$m in say 5s is not physically impossible.
Diffusion in still air over distances of 400m usually takes a few hours rather than seconds, so I think that advection (the bulk movement of air) is likely to have been the dominant factor in the reported cases (as you suggested). Windspeeds at 10m above ground are typically 5m/s, decreasing downwards, so a transport time on the order of 100s is reasonable. Strong winds would reduce this time, but the descriptions "within seconds" and "almost instantly" seem somewhat exaggerated.
Obviously environmental conditions could prevent any substance being detectable at distance (wind in the wrong direction etc.). So, assuming the conditions are not against a substance being detectable, what makes Thioacetone so detectable (compared to other substances)?
From the Wikipedia page the key factors seem to me to be:
The trimer of thioacetone [...] with a melting point of 24 °C, near room temperature
It will dissipate into the atmosphere very easily. It was also found "that dilution seemed to make the smell worse". Note as the side-box on that page states, the melting point of thioacetone itself is 40 °C.Like many low molecular weight organosulfur compounds [...]
Low weight will allow it to be carried for longer distances without sinking to the ground.[...] the smell is potent. And like such compounds it can be detected at high dilution.
Only very small quantities need to make it to your nose. The "sphere of detectability" will be much larger than for other compounds.
In other words, what makes one particular substance more detectable ("smelly") than an other is how easily its molecules can enter the air, how widely they can be dispersed without settling and how detectable they are if they reach your nose.