It certainly looks as if the variable plotted along the X axis can only take certain discrete values.
However ... a categorical variable is one that takes values in a sample space where neither magnitude nor order have any meaning. Example: a medical study might record the gender of the patient (male/female), which is categorical .. the age (which is numeric) ... and which of several possible OTC cold medications they took -- also categorical.
A categorical variable could have infinite support --- imagine sequences of letters from the Latin alphabet -- of arbitrary length. You have an infinite number of possibilities -- all categorical, because there is no natural way to measure the distance between them, or to rank them (although we could come up with a few).
Contrarywise, a numeric variable could admit to a discrete number of possible outcomes -- such as the spectrum of a particular chemical element.