Here is an example where Harvard Stem Cell Institute discusses mRNA therapy as gene therapy: https://hsci.harvard.edu/translation/what-are-drugs-4-gene-t...
The Wikipedia entry on gene therapy discusses mRNA therapy under the Non-viral section: https://en.wikipedia.org/wiki/Gene_therapy – “BioNTech, Moderna Therapeutics and CureVac focus on delivery of mRNA payloads, which are necessarily non-viral delivery problems.”
Indeed the mRNA vaccines carry a genetic payload – a segment of viral genome which is modified using a genetic perspective and from a position of genomic understanding. mRNA is a temporary and deliberately non-permanent message carrier substrate; Here too, humanity’s employment of such facts can be interpreted as scientific knowledge of the matters of the genes. If we choose to call mRNA vaccines gene therapy – which they are less clearly than other techniques – then it is certainly the better gene therapy for purposefully avoiding permanent alteration of the genome in the subject to be treated.