You have it right.
N-reg are governed by FAA rules, worldwide.
G-reg are governed by CAA rules, worldwide.
In this case, the CAA requirements are specific to G-reg. I don't recall how the ANO defines this but IIRC you will find there is a group reference to some annex which, if you read it, is basically "G-reg".
Other requirements, e.g. equipment carriage like ADF, DME, Mode S, is applicable to any reg flying in UK airspace.