That's right - an DPDT switch is really just two SPDT switches that move together - in the diagram, the top part is one SPDT switch and the bottom is another, the fact that they move together is what makes them a DPDT switch. You don't (usually) need both poles in this sort of situation, but it does no harm to have both, and costs little extra in materials or effort.
It can be a matter of preference whether you have the centre-off position or not - it does no harm and can be useful, too.