Why do they always say the entire quadrant is at stake, when obviously the entire Federation combined with the Romulans, the Klingons, the Cardassians, the Breen, and the Ferengi is still a small fraction of the Alpha quadrant.
You're absolutely right. The quadrants of the galaxy are very large and the superpowers of the Alpha Quadrant represent only a very small proportion of that space. On top of that, the Federation is continually discovering entire solar empires within their own borders, so they can't even claim to be fighting for the whole of their own territory, let alone on behalf of the entire Alpha Quadrant.
What you're looking at here is a mixture of hyperbole and simplification. Assuming the Dominion force can flood freely through the wormhole, it's likely that once they've dominated the Federation, Klingons and Romulans that they'll attack other states outside the current known territories of the Alpha quadrant superpowers.
Map courtesy of Star Trek: Star Charts