In the Card Explanation on page 24 it reads
Remingtion Roomsweeper: You determine which obstacle Remington Roomsweeper damages when you apply damage. Once you start applying damage, you choose a runner and Remington Roomsweeper does damage to all the obstacles and bosses facing that runner. Use counters to mark the extra instances of the Remington Roomsweeper damage. If you play a Katana on the same turn as Remington Roomsweeper, the damage to every obstacle of boss that Roomsweeper damages is increased.
...
Actually, there is a small mistake with that quote. Trust me it is easy to miss, as I read it 5 times in the last 3 days before I spotted it.
Remingtion Roomsweeper: You determine which obstacleS Remington Roomsweeper damages when you apply damage. Once you start applying damage, you choose a runner and Remington Roomsweeper does damage to all the obstacles and bosses facing that runner. Use counters to mark the extra instances of the Remington Roomsweeper damage. If you play a Katana on the same turn as Remington Roomsweeper, the damage to every obstacle of boss that Roomsweeper damages is increased.
That first sentence really emphasizes the fact that this is supposed to be able to affect more than one target, and you have to really parse this paragraph carefully to get its meaning.
- You determine which obstacles Remington Roomsweeper damages when you apply damage.
Basically, you put out the card and say "I will use this for damage." No targets have been chosen yet, as the Damage Phase has not started yet.
- Once you start applying damage, you choose a runner and Remington Roomsweeper does damage to all the obstacles and bosses facing that runner.
So you never choose a target for this card
per se. You simply choose a runner and every thing in front of it takes the Roomsweeper`s damage. So the answer to the OP is (B). At least as far a I can tell.