includes any and all changes in cell's genome. When viral DNA is integrated into the host cell genome which is normally (perhaps not exclusively) the case with HPV, you essentially have a cancer causing gene / genome alteration brought on by viral infection. Now in such cases, it is more appropriate to use the term oncogene acquisition: v-onc to c-onc, to set the distiction. However it is not wrong to say that the resulted cancer or any cancer is disease of the gene (or of the genome, of the DNA).
If you have better case of cancer not causing by somatic DNA mutation (or genome alteration), I am wide open to hearing it.
