Not really. The number of people who might change their minds and thus swing the result either way is indeed small. But it isn't accurate to say they are the ones that choose.
The people in guaranteed states/counties still choose; it's just that almost always choose the same answer.
But even that doesn't mean they can be ignored. They can be ignored at voting time, but before that political parties have to take them into account. They basically determine where the centre is. For example they are the reason the American centre is so much further right than the UK centre.
If you took American parties and held an election of them in the UK you would find that all those reliably conservative counties who you would say don't have any effect on the result are suddenly not so supportive of the right-wing option.
FPTP is still dumb and frustrating though.
