Yes, prospero, but doesn't 'game' suffer from the same nounal problem in the sense conveyed here? In my first post I said I was unsure of the accuracy required because I hadn't tackled a Genius puzzle before (I know The Listener has rules about the practice we're discussing here). Similarly, the use of capitals in another clue sacrifices the accuracy of the definition to the surface reading (the two groups in uniform) and there are rules about that too - although I'm perfectly happy to see the rules broken in a good cause.
There are umpteen possibilities in this kind of 'clue' ('Apache' in the French sense isn't a million miles away if we're looking for a 'rat' - and then 'an' can be used - but it's a very loose synonym).
The point is, if there isn't a cast-iron way of reading this sentence, then this 'clue' isn't working in the way that most of the others do. Everything written about this one so far is more or less flawed, in my opinion (as I tried to suggest from the outset, in reply to a question from you) so querying the details just adds to the confusion.
I think you're right to keep looking and I hope to see a convincing answer at some point - I'll (quietly) enjoy the moment.