Reptile, I agree entirely with your analysis. The FCTM is remarking on failures to a serviceable aircraft, not one already on a single engine.
If a fire below 1000ft is going to compromise a safe landing you'll stand no chance whatsoever if you launch into another circuit, if it won't compromise a safe landing then that is what you'll get, and the fire service won't need those 500ft ladder extensions.
In any case, as flyhardmo says, what are you going to do with the burning engine? The only part of the fire drill you can do is to fire the fire bottles - you can hardly shut it down. (indeed, in a g/a you are asking the burning and presumably damaged engine for TOGA thrust - hardly a sensible thing to do under the circumstances).
The scenario itself is farcical. This is double jeopardy and is not a realistic or practical exercise with any training value and its inclusion an assessment or check tells one a great deal about the mindset of the airline involved. In the case of double jeopardy you may have to extemporise. I'd fire both bottles into the burning engine, make a radio call and land and stop as quickly as possible with almost certainly an evacuation on the runway. If you've already had an engine shutdown and then get a fire on the other one the "instructor" is likely to throw a meteorite strike or earthquake at you on the runway for good measure. I'd get out and run away as fast as I could! (from CAAC as well)