If you read the linked article,
you may arrive at this conclusion.
Sounds like they had a hung, or maybe even a wet, start, and were then left pushed back with one engine running and needed to shut down, wait and then attempt a re-start, with the inevitable delay that would create from missing their slot, etc, etc.
My guess is the question asked was probably would the passengers want to sit on board for a while whilst they tried to sort things out, or would they prefer to disembark and get a later flight.
The question being asked seem to be 'do you want to stick with this aircraft, and maybe the engine thing gets sorted out, or will you try your luck with getting on another aircraft'?