"Personal use" and "non-commercial use" are not statutorily or (I would presume) contractually defined terms. One (preferred) approach is to ask the property-owner whether a product can be used in a particular situation. Another is to try to interpret their statement the way common sense (vaguely defined) tells you that it should be defined. One interpretation – completely wrong – would be that you can use the product in any way you want, as long as you don't charge customers for using the product. But nobody charges customers for incidentally viewing computer wallpaper. Computer wallpaper is for the benefit of the individual using the computer. So whether or not a company has a public showroom with walk-in customers who might incidentally view the wallpaper, such a use would clearly be in the context of a commercial enterprise, thus a commercial use. And that is what is prohibited.
The meaning of the combination "personal, non-commercial use" does get a little murky when applied to an imaginably non-commercial setting such as a non-profit organization, a government office, or a library. Such uses are (generally) not commercial, but they are also not personal. The ordinary language interpretation of adjectives strung together like that is that an "and" is implies -- the use has to be both personal and non-commercial. That would mean that using the product in a government office (etc.) is also not permitted.