Qualified person means one or more of: worker; self-employed; student; self-sufficient; jobseeker.
'Gap year working in UK' just means 'working' to me. So if any of this work took place before May 2011, was son registered fully and properly for WRS?
Otherwise his time as a worker can only have started in May 2011 (when WRS ended).
Yes, CSI = comprehensive sickness insurance.
Whether son needed or had WRS is probably academic anyway as the lack of CSI during son's real academic years, at uni, pose a major problem,
His PR clock probably won't have been running if no CSI and no EHIC whilst a student.
That means all previous time in UK (for A levels, gap, uni) is lost in terms of acquiring PR.

Its a longshot but one way to save this period (and make it count towards PR) is if son had had the foresight to apply for a RC issued to him
as a student in/before 2011.
Not sure how the timeline works out on that one, you are best-placed to know.
Did son have such a RC?

Otherwise another way to rescue son's time spent in UK is to see if he can be considered to have been sponsored by an EEA parent who was a qualified person at the time; (cohabitation not necessary).
Was this the case?
Note If son was over 21 at any time he will have to prove financial dependency on this sponsor.
(That's not necessary for any time being sponsored by a parent whilst under age 21).
With a viable sponsor (and rock-solid proof of dependency for any time son was over age 21,
in fact rock-solid proof is required for all 5 years) its just possible son has acquired PR by being sponsored whilst doing A levels, gap year plus say 2 years of uni.
If son has blown it with the university years one could argue he may as well stay teaching in China.

But there are one or two provisos.
Be aware that if he stays out of UK for
over 6 months (based on anniversary of arrival in UK), and certainly if he stays out
over 12 months (for a one-off exceptional reason), his
continuity of residence will be ended.
That means when he returns to UK his PR clock will have to restart from zero (again).
If this is the case, son obviously won't now have time to acquire PR in the normal way (as
Brexit final exit is looming).
And since end of last year possession of the optional and
confirmatory DCPR has been made one of the
mandatory prerequisites for the privilege of citizenship.

If/when back in UK, son will have to rely on the
traditional British sense of fair play and any
transitional arrangements that may be put in place for EU citizens; (all yet TBC ofcourse).
But do be aware of recent comments in press (from ministers) talking about a cutoff date for 'late arrival' Union citizens who now come to UK.
If son has lost
continuity of residence he may fall into the category of a new arrival rather than someone who has been here 7.5 years.

On this basis, it may be prudent for son to come home and at least apply for a RC / EEA (QP) if his future is to lie in UK.
(fyi - the UK's EU-related transitional arrangements often depend on having EU documentation at a certain key date so that could prove a worthwhile investment of £65).
Finally, there's a mix of EU and UK domestic requirements that all need to be balanced up and met in full.
a) being away from UK over 90 days in the year before applying to naturalise will push back and delay when one could apply for the privilege of citizenship.
and
b)PR status (not necessarily having a DCPR) has to be held for 12 months
before applying to naturalise (unless married to a British spouse).
(Its 6/12 months absence that stops the PR clock not 4 months).