You shouldn't only look at the first definition, even though that is the one that deals with utensils.
The next part of the definition you linked is:
1.2 Pick up (someone or something) in a swift, fluid movement.
‘he laughed and scooped her up in his arms’
In your sentence
She scooped up a little ball of rice with her chopsticks.
scoop is being used to emphasize that she is proficient with her chopsticks. She can swiftly and easily eat rice with them, something that people not skilled with chopsticks have a hard time doing.
You could also say something like:
Into our mouths, we shoveled rice bathed in sauces that glowed red and gold and smelled of a potpourri of balmy spices. (Source)
That doesn't mean that we ate with shovels, just that it was so good we ate very quickly (and maybe ungracefully in our haste).