Well, many things come here into play.

1) This is an animations studio. Many things are still done by hand - so they have lots of paper, paint, ink, etc you name it. Everything produces toxic smoke

2) Animations studio usually is an open space, pretty damn cramped to begin with and with lots of tools, tables, source materials and other things lying around. I'd imaging it is not the place you will find most suitable for an emergency evacuation.

3) People were going up. So did the smoke. It takes you just a few deep breaths to lose consciousness. It is possible they simple didn't even make it to the door.

Not necessarily - dying in badly ventilated staircases is a very common cause of death during fires in large buildings. During a mandatory fire safety training I was told that often it is better to stay in your room, close the door to the hallway (treat it as a fire barrier) and go to the window where the firefighters can come get you.

What I heard / read is that the perpetrator blocked the emergency exits.

There are rumors going about the arsonist jammed/ignited the fire escapes closed before the attack

Japanese buildings also are massively lacking in emergency exits. Almost no building would pass US safety codes or even come close to it.