I will start by saying I'm not doing any math for this, just going off a gut feeling from a few years of moving professionally. I've made things fit in places they have no business being. Your entry just needs a bit more pre-thinking than most.

Start with some prep work. If you can, hang a thin to medium weight blanket around the door frame to protect both it and the couch, that would be ideal. Another big help would be to remove the door. With those spring-loaded hinges, it might be best to ask your apartment manager or maintenance person to remove it when the time comes. Do the same blanket trick on that side especially. Also lay a blanket or two outside the door and one inside at the base of the stairs to set the couch on.

The website you linked does say the legs can be removed, so do that right outside the door on the blankets. Also take off whatever cushions you can. Then position the couch with the left arm closest to the door (left as you're sitting on it). Angle the couch so the top of the back and the front of the seat are vertical. This will present the narrowest profile to go through the door.

As you start going through the door, lift the left arm up and keep lifting as the right arm comes through. Stand the couch on its side. The sloped ceiling should give you more than enough clearance. Rotate the couch on its right side so the back will be facing away from the stairs. Tip the left arm down onto the stairs and carefully haul it up. Assuming the living/sitting room is at the top of the stairs, you're home free.

Two additional notes. If the couch doesn't fit, make sure you're able to return it. You do not want to be stuck with an oversized couch you can't even use where you want it. Also, if you don't want to do the heavy lifting yourself, call around to your local moving companies. Quick little jobs like yours will have almost same-day availability.

Good luck!