Hereis the article discussing the DNA analysis - not behind a paywall for once. A detailed description of the phalanx is in the Supplementary information - Section 12, p. 83.
The bone is very small, from a young individual, estimated 6-7 years old so the ends would not have fused, and the bone is incomplete. The researchers say this makes it impossible to determine which finger the bone came from, and they make no mention of handedness as a result.
Bones in your midline axis [skull, vertebral column, pelvis] are symmetrical, but your other bones are not. The phalanges are asymmetrical, but its pretty subtle and it helps to have complete specimens from mature individuals to determine which hand and digit. From the sound of it there was not enough present to make a firm call as to left or right.
Maybe there is an unspoken convention that palaeoanthropologists only show the right hand, like shoe shops only displaying right shoes, so you can’t swipe a matching pair from two stores?