The IMG_xxxx.dng files are from the G5 X and the DSC_0134 is from what camera?
Are you hoping she can work with the DNGs in Aperture or a trial of Lightroom? The screenshot seems to be the OS, not either of those programs, right?
Last I remember Apple didn't know how to parse DNGs that had the op-codes for built-in lens profiles. Maybe that's changed, and maybe an older DNG-compatibility conversion setting used in the DNG conversion process would make them work? You could certainly reconvert the DNGs with the standalone DNG Converter program after changing its DNG Compatibility options to something much older than the ACR 7.1 that it defaults to. Not having a Mac I don't know if this works. I expect Rikk is wanting to see if you're doing anything else in the DNG options that would confuse the OS preview renderer so do post that screenshot he's asking for.
Assuming you don't have any of the original raws, anymore, use the DNG Converter to make new DNGs from the old ones, but undo the Embed Fast Load Data and try much lower numbers in the DNG Compatibility area.
These are the two settings I'm referring to as illustrated in your LR DNG Conversion options:
In the DNG Converter, which you'll actually be using, these settings are in its Preferences area:
Don't discard your original DNGs, because you'll want to run the conversion more than once, to determine the latest version of Compatibility level, if any, that allows the Mac to view the previews, and then see if that will work for her in Aperture.
And maybe you've done all this but the sentence "working with the DNG Converter doesn't help" isn't specific enough to know.
The Mac must need to have camera-model support and ignores any raw format, including DNGs, it isn't programmed to recognize based on the camera model. DNGs are created to work with Adobe software that is too old to have camera support built in, but not necessarily anyone else's software, including Apple's apparently.