It looks like it doesn’t modify DNA, but it does modify what was just transcribed from the gene by removing an exon from the corresponding mRNA that came from the gene.

The source describes the 4 molecules the virus injects:

We developed a therapeutic exon skipping viral vector (scAAV9.U7-ACCA) comprising four copies of a modified U7snRNA containing antisense sequences targeting the splice donor (2 copies) and splice acceptor (2 copies) of the DMD exon 2, the most commonly duplicated exon.

It looks like it doesn’t modify DNA, but it does modify what was just transcribed from the gene by removing an exon from the corresponding mRNA that came from the gene.