mRNA (messenger RNA) is the "working copy" of gene that the machinery in the cell's cytoplasm uses to direct synthesis of a protein (translation). Thus, if you can get a suitable-looking mRNA into the cytoplasm (e.g. by coating it with NLP), the cell will start translating it.
DNA, on the other hand, first needs additional machinery to make an mRNA working copy from it (transcription), which process takes place in the cell's nucleus. It's much harder to get things into the nucleus from outside the cell. Adenoviruses are not only robust (hence their long shelf life under refrigeration), but as double-stranded DNA viruses they are already specialized to get their DNA contents into the nucleus and get it transcribed.
It's all a matter of the right tool for the job.
Edit: Regarding transport of the viral DNA into the nucleus, here's part of an abstract from a relevant paper: ("Viral entry into the nucleus" PMID: 11031249 DOI: 10.1146/annurev.cellbio.16.1.627)
"Because many viruses replicate in the nucleus of their host cells, they must have ways of transporting their genome and other components into and out of this compartment. For the incoming virus particle, nuclear entry is often one of the final steps in a complex transport and uncoating program. Typically, it involves recognition by importins (karyopherins), transport to the nucleus, and binding to nuclear pore complexes. Although all viruses take advantage of cellular signals and factors, viruses and viral capsids vary considerably in size, structure, and in how they interact with the nuclear import machinery. Influenza and adenoviruses undergo extensive disassembly prior to genome import"
Just injecting DNA into the cytoplasm won't do much of anything - a lot of machinery is needed to get it to and into the nucleus, some supplied by the virus and some supplied by the cell. NLPs have none of that.