Does training adolescents require a different approach with regard to the level of neurological development?
No, that article doesn't suggest a different training approach with teenagers.

What it does suggest is that the teenage brain has potentially more neuroplasticity, and that "the capacity of a person to learn will never be greater than during adolescence." It does point out a possible factor to watch out for in young trainees: sleep deprivation, but it doesn't say that the effects of sleep deprivation are different than in older trainees, only that they may be more likely to stay up late.

The article mentions "the importance of creating an environment in which teens can explore and experiment while helping them avoid behavior that is destructive to themselves and others". Flight instruction seems to me to be exactly such an environment.

Instructors already should be adjusting their training approach to the individual. (Transport Canada - Flight Instructor Guide: Individual Differences). The advice given is based on symptoms, and there is no indication that a teenage slow learner (for example) should be treated differently than an adult slow learner. There is a column in that guide relating to "immature" trainees, which might apply more frequently to adolescents, but unless a student is showing immaturity, there is no need to treat them so.