It's not seen as a "real" job by many out of the industry - just look at other threads on here, they are just playing at games😂
It's actually a very technical and skilled industry and role.
I would recommend they do a broad range course and not just games design, this opens up the doors to Microsoft, Sony etc and there is a huge development in the industry around artificial intelligence, virtual reality etc. It's not just games design but software design, how it can be used to support practical training - car maintenance through virtual reality. (They would for instance, create the Microsoft holo lens and all the packages and workplace support to go with this).
Particularly look for ones with programming, vfx and high spec software usage.
These are very practical and hands on courses.....the former polys are good at delivering these and the work places are screaming for all round staff to train up.
You won't find the red brick offering these as much....perception of the course again!
Industry won't hire the person who plays his Xbox all day in the basement and thinks they can be a games designer. Hence the shortage - the perceived role and skills vs the actual skills and role.
(My teen is similar to yours, comp sci and engineering all the way - I very much expect him to go this route too).
Not sure what stage you are at for options (gcse, post 16 or uni) but go and look at the courses at the next stage and get a feel for them and work backwards. Lots of colleges offer the level 3 games diplomas (btec, ual, aim, ocr etc..... they are all very difft quals, I work with one of the qualifications and would always sell that one over others....but it's geographic to what's on offer near you).
Most of the learners on these courses go to apprenticeships with big names (ea, unity, Ubisoft, Sony etc) or uni degrees. (Royal hollowell, abertay, Dublin, Belfast, Teesside, there is one in anglia, can't remember name off top of my head just to name a few). Pay and opportunities in industry are high.