No, Richard Dawkins did not invent the term.
"Lord Privy Seal" is a reference to a parody of the practice performed by David Frost, on The Frost Report in 1966.
Since then, the trope has been known by other terms, such as B Roll Rebus.
Webster's Online Dictionary acknowledges this usage and the etymology:
> The term "Lord Privy Seal" (as in "not bad, but it's a bit Lord Privy Seal") is used in the British television industry as shorthand for associating pictures too closely and literally with every element of the accompanying spoken script
Webster's seems to rely on the memoirs of BBC insider, John Sergeant, _Give me Ten Seconds_ , for the usage.