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Sure, the shape is helical, but the official term for these constructions is “spiral staircase” whereas the official term “helical staircase” refers to something else.
Sources: [One](http://www.salterspiralstair.com/?gclid=CjgKEAjwq_qcBRDZ-PeZ7NGQiVwSJAATT7q2cH5QDTdRMyx-DPj_wifqp0V75o3Ru-DI7A52lk3r9vD_BwE) [Two](http://www.mylenstairs.com/?gclid=CjgKEAjwq_qcBRDZ-PeZ7NGQiVwSJAATT7q25GjT7GKAKtGEkuOuB5Mw-u4tK2Y6K_b1aoQ_zEaEzfD_BwE) [Three](http://www.lowes.com/Building-Supplies/Stairs-Railings/Stairs-Accessories/Spiral-Staircase-Kits/_/N-1z0ynvd/pl#!) [Four](http://www.elitemetalcraft.co.uk/publish/Gallery%20Staircases/Helical%20%20Staircase.html) [Five](http://www.stairporn.org/tag/helical-stairs/)
In the DEFINITION of Helical Staircase: “Helical staircases differ from spiral staircases as they do not have a newel, and handrails are present on both sides. ”
OP’s picture has a newel. It has handrails only on on side. It is a spiral staircase.