Dominant chords are a 'family' of chords...there are essentially three families...Major, Minor, and a bit of both...Dominant. Beyond that there are other chord types...diminished, augmented, sus, etc...

The V chord of key just happens to be built to a 7th chord. It's the fact that it's the V chord that forces it back to the one, not the fact that it can be built with the b7.

It's evident in the 'b5 substitution' when they say 'a Dominant chord can be substituted with a another Dominant chord a b5th above it'.

That substitute chord is not the V of the key, but it is still a Dominant chord.

Also, in chord formula's they are not concerned with the key or the V, or whatever...they are concerned with the fact that a Dominant chord, or the Dominant family, is built with a 1 3 5 b7.

Again, the V chord of a key just happens to be built with a b7.