The armrests end up at about waist level. Spillover could be above the armrests or below them, depending on the individual passenger's body composition. Because we are all three-dimensional, it can't be determined in advance which, if any, passengers will need two seats. Southwest's Customer of Size document seems very clear to me on this.
The decision to purchase two seats in advance is entirely up to the passenger, based on the guidelines and information provides by Southwest along with any information one can garner online. As indicated above - if the passenger opts to purchase two seats and there is even one unsold seat on their complete itinerary, Southwest will refund the second ticket after the flight. Instructions are available on the website.
Alternately, the passenger could purchase a single ticket. If, on arrival at the airport, the Gate Agent determines that the passenger may not or will not fit completely in a single seat with the armrests down, they will ask the passenger to preboard and will test the ability to fly fully in a single seat. If the passenger can fit in the one seat with the armrests down and not 'overflow' into an adjacent seat or the aisle, no harm no foul - AND the passenger has preboarded.
If, on the other hand, it's determined the passenger needs a second seat, they will be required to purchase one. If there isn't an additional seat available on that flight, I forget what the exact restriction is - whether someone else would be bumped, or if the Passenger of Size will have to take a later flight.