Actually, it's a bit more complicated than all that. There are many different definitions of deserts, each one pertaining to the purpose of the word in that context. Meteorologists and Geologists classify a desert as a place with less than 10 inches of average precipitation (in terms of rainfall) per year. Biologists consider a desert to be any biome where the evaporation rate consistently exceeds available precipitation. By both of these definitions, which are as valid as any other within their given contexts, the Sahara still is the largest. Precipitation also comes in the form of snow after all.
This only considers two legitimate definitions of the word desert, as it applies to terrain. The common definition of a desert is in and of itself a valid definition as well. If two laypeople are talking about "deserts", they know precisely what they are talking about: hot, dry, sandy and/or rocky places. If the need arises to use one of the more esoteric definitions of desert, one or the other of the people conversing will clarify and limit or expand the definition as needed.
Asking about the "largest desert" on a quiz is just one of those instances, the quiz-writer should phrase the question to frame the definition of desert that he/she is looking for. Getting tied up in semantics defeats the purpose of effective communication, and being too nit-picky about dictionary definitions usually serves no good purpose.
Look at two songs using the word desert, America's Horse with no Name, and The Eagles' Peaceful Easy Feeling.
I've been through the desert on a horse with no name
It felt good to be out of the rain
In the desert you can remember your name
'Cause there ain't no one for to give you no pain
La, la ...
After two days in the desert sun
My skin began to turn red
After three days in the desert fun
I was looking at a river bed
And the story it told of a river that flowed
Made me sad to think it was dead
And the Eagles:
I like the way your sparkling earrings lay,
against your skin, it's so brown
and I wanna sleep with you
in the desert tonight
with a billion stars all around
'cause I gotta peaceful easy feeling
and I know you won't let me down
'cause I'm already standing on the
ground
In both of these instances I seriously doubt that anyone pictures an ice-sheet in Antarctica.