When people talk about the “gateway effect” of e-cigarettes, they are usually referring to the first gateway: the fact that never-smoking kids who initiate nicotine use with e-cigarettes are more likely to start smoking cigarettes than youth who never try e-cigarettes.
E-cig enthusiasts dismiss these studies by invoking the “common liability” theory which asserts that the kids who start with e-cigs would have started with cigarettes anyway had e-cigs not been available.
While it is true that some kids who start nicotine with e-cigs have risk factor patterns similar to kids who start with cigarettes, several studies have shown that a substantial fraction (around half) of kids who start with e-cigs have risk factor patterns that make it unlikely that they would ever pick up a cigarette. (See this paper and the other work cited in it for the detailed statistics.)
The fact that there are a substantial number of kids attracted to nicotine addiction by e-cigs who would likely never start with cigarettes is the second gateway: e-cigs are expanding the tobacco epidemic: By attracting kids who likely would never start nicotine with a cigarette or other tobacco product.
Beyond the detailed statistical analyses of the characteristics of kids who start with e-cigs or cigarettes, this second gateway is obvious from the fact that after e-cigs came on the market total youth use of e-cigs + cigarettes shot up, with the increasing number of kids using e-cigarettes far outstripping the decline in cigarette use.

These two effects combined in e-cig-friendly New Zealand, where not only has youth e-cig use skyrocketed but declining cigarette use stopped and is now increasing, likely because of the first gateway effect.

Indeed, in our analysis of patterns in the US through 2018, we found that the introduction of e-cigarettes was followed by a slowing of the decline in current cigarette smoking.
And, even if the kids who start with e-cigs never add or switch completely to cigarettes, it’s still good for tobacco companies and bad for health.
Research and policy discussion of e-cigs and kids needs to consider both these effects, as well as total tobacco product use, taking into account dual use (using both products at the same time).
Of course, getting rid of e-cigs will close both doors.