to quote another bit of that opening link:
The committee advises ex-ministers on taking new jobs after they quit.
It does this based on rules aimed at avoiding the risk of a former minister "improperly exploiting privileged access to contacts in government" and the suspicion that a new job is "a reward for past favours".

Boris has already said he won't be exploiting information he received in his ministerial capacity. As for the new job being "a reward for past favours", he is just taking up where he left off when he became a minister, so hardly a new job, even if it did need a new contract.