The one legal right S'mon doesn't mention is 'right of personality'. I hadn't heard of it until the Law of the Geek podcast had an episode on it. Its protection is based in state law in the US, so it is hard to predict how it would apply here
There is no 'Personality Right' in UK law. It can be said that the UK courts may take an expansive approach to the law of Passing Off (requiring Business Goodwill, Misrepresentation, and Damage per Jif Lemon) where there appears to be a misappropriation of a celebrity image - see Irvine vs Talksport; in that case Talksport used an unauthorised photo of Eddie Irvine the racecar driver to advertise their talk radio station. This was based on Irvine having an endorsement business.
Conversely in Stringfellow vs McCains the strip club owner Peter Stringfellow was unsuccessful in suing the food producer McCains for their "Stringfellows" long & thin chips, Stringfellow had no endorsement business to harm.
In this Gygax Magazine situation, I don't see any Misrepresentation given Luke & Ernie's use of their own name. I'm not sure whether the Gygax Estate has Business Goodwill in the Gygax name, it's not currently used but has been used in the past (to a limited extent) - a UK court could go either way, but I'd suspect they would say it does have Goodwill.