In respect of this particular study there may be only very limited room for direction of young people to other specialisms without first going through paediatrics. There are two substantive limitations -
Firstly to be counted in the study the young person must be effectively absent from school which implies a specific legal status (UK Law requires full attendance for specified hours) so a child not attending school at all will have the involvement of Local Education Authorities - social workers etc, who will liaise with the GP and provide a bureaucratic impetus for involvement of paediatricians in the case.* Secondly the NHS is heavily stratified between adult and paediatric care and it would be rare for a GP to refer a person under the age of 16 to a Specialist service where there was lack of clarity about the diagnosis - and in the case of ME/CFS the few specialist services that there are, either see adults only or have a separate paediatric service for younger patients.
The combination of the involvement of schools and education professionals in cases of long term absence plus the extensive paediatric provision in the NHS means that the services the authors surveyed are likely to capture a high proportion of young people who have an ME/CFS diagnosis and who are permanently absent from school.
*This situation is not always welcome by parents who can face undue pressure re: return to school and/or bureaucratic psychologisation of their child's illness.
Clearly this is just a single study and it doesn't tell us about alternative diagnoses but the Education data sets limits to the significance of this, basically there's a limited number of young people permanently out of school for reasons of illness and it's hard to see where many more young PwME would fit in.