You definitely have interval data, that is, data which takes on discrete values, as opposed to continuous data, which takes on values along a continuum.
It may be of value to additionally determine if the data is ordinal, meaning that the order of the values is important, for example if [0, 1, 2] signifies [small, medium, large] or some analogous system.
In the case of ordinal data, it may be best to keep the data as exposed to the SVM training process in integer form, as the integer representation encodes some information about the relationship between the categories.
This approach would also be more reasonable if the values that the variable could take on in a production setting could expand beyond the values you've already observed in the training set- a categorical approach would be less able to handle new values in that context.
If there are no ordinal relationships and you suspect all of the possible values are enumerated in the training set,treating the variable as categorical would be approriate.
It looks like counting data to me. Without further information in the question, I'd keep it as a categorical data and model it with discrete techniques (e.g. Poisson GLM)