nooka, firstly, apologies - you are quite correct, I misread the first study you posted. In fact I was thinking of a quite different study that I can't even find now (there are so many of them!)
There is expert reaction to the study you posted here. Also see CRUK's take on it.
The study only measured 'ever use' not regular use. It could be that children only ever tried either smoking or vaping, or both, once. The study also does not tell us whether the children were using ecigs with nicotine.
Our findings also indicated that the association between ever use of e-cigarettes and initiation of cigarette use was particularly strong among adolescents with no friends who smoked
But this is not really surprising. Those with friends who smoke are far more likely to have smoked a friend's fag first if they wanted to try it. Among those who tried smoking but who did not have friends who smoke, 49% had tried an ecig first, 51% hadn't. As Bauld says, Which came first – and why – might simply be a matter of chance, rather than anything else.
While it controlled for some covariates there were some important ones that were not controlled for. In fact the authors themselves acknowledge this: our research could only consider a finite number of covariates and moderators, and it is plausible that important factors were omitted. Previous related studies16–19 have examined various other factors (eg, sensation seeking, impulsivity, other substance use, delinquent behaviour, academic performance and race/ethnicity). (in fact, the discussion section of this study is full of limitations and caveats)
We know that there is a strong relationship between youngsters trying one substance and trying another, whether that is cigarettes, ecigs, alcohol or other drugs, in fact risky behaviours of all sorts tend to cluster together and this is where 'gateway' theories fall down - how do you pick out causation? Young people experiment with things and some experiment more than others.
There is a good discussion of the problems with gateway theories in PHE's report (from p37). I won't C&P it all here, but they conclude We strongly suggest that use of the gateway terminology be abandoned until it is clear how the theory can be tested in this field.
If ecig use among either adults or children led to smoking we would expect smoking prevalence to increase as the rates of ecig use increase. All the evidence points the other way. Wherever you look, smoking prevalence among children continues to fall at least as fast as before ecigs became popular. Above is a graph showing youth prevalence of smoking in Connecticut (PDF link), where your second study was conducted (which frankly I don't have the time to pick through). If, as the authors assert, Electronic cigarette (e-cigarette) use rates are high among youth (they're not - regular use among never smokers of any age remains extremely low) and if vaping leads to smoking, then where are all the extra smokers?
Of course PH specialists are keeping a very close eye on this issue but the reputable among them will of course focus on overall prevalence rather than small studies based on a flawed 'gateway' theory.