What risks come from passengers taking baggage during emergency evacuation?
As soon as there's a fire on board, the absolute top priority is getting everybody out as soon as possible. Aircraft are designed in such a way that, even after a crash landing (or other serious malfunction), the passengers will have a minute or two to evacuate before conditions in the cabin become toxic (fire, smoke, etc); this is done by using flame-retardant material and burn-through protection, but in an intense fire these won't protect the cabin for long, and once they fail no-one will be able to survive inside the aircraft for much longer than that. Smoke inhalation and oxygen deprivation kill just as effectively as being burned. 

Therefore everyone has to be able to evacuate from the plane within 90 seconds, even assuming the plane is packed to the gills with passengers, and half the exits are inoperative. Given that the aircraft may be damaged after  a rough/crash landing, some of the doors may be unusable (due to fire or smoke just outside them), it may be dark in the cabin, and people may be injured and/or panicking, it's vital that nothing slows down the evacuation. To get an idea of what a 90-second evacuation of a fully-loaded aircraft looks like, see the video of the A380 evacuation test - and these passengers were calm, uninjured, and prepared. If passengers take hand luggage with them this is slowed down:


The time it takes to get it out of the overhead bins (with everyone else crushing against you to get out).
Carrying the luggage down the aisle (without tripping, hurting yourself or anyone else - again, look at the A380 video, and imagine trying to do that with a suitcase). If you lose your luggage, everyone behind you will have to climb over it to get to the exit.
Maneuvering your suitcase around the corner to the door, not getting it stuck on the door frame, with people behind you literally shoving you out the door.
Plunging down a very steep slide the height of a two-storey building (or more, in case of the A380's upper deck) at high speed, with your suitcase flailing around. At best it whacks you on the head, at worst it punctures and deflates the slide, which given the crush of passengers behind you will probably lead a few people to plummet from the aircraft doors straight to the ground.
Assuming you've made it to the ground, there is someone else plunging down the slide right behind you. If your suitcase slows you down even a little, they will plow right into you, and soon you'll have a crush of people at the foot of the slide.


In this specific case, the fire was fortunately not serious enough to defeat the cabin fire protection before the last passengers had evacuated - but as @Andy said, there are unfortunately other examples where the passengers were not so lucky. To illustrate the risk of fire after landing: Air France Flight 358 ran off the runway at landing, and despite having little fuel on board, the resulting fire completely destroyed the aircraft; luckily, everyone evacuated in time. Once there's been a major malfunction, there is no way to tell how much time you have left to get out - fire can spread very very quickly - and so you have to get out as quickly as possible. Taking luggage with you endangers your life and that of your fellow passengers.