I guess an inorganic glass is a glass that does not fall under the much more recently invented class of materials known as organic glasses, which are essentially glasslike polymers. So all traditional silicate glasses are inorganic glasses.
Inorganic glass are considered as alloys with inorganic oxides as compounds.
When a meterial is rapidly cooled(the cooling rate is higher than a critical value), the material will not form to solid but liquid. The state after this rapid cooling is called supercooled liquid, because it has passed through the freezing range. And it transforms to glass.
It is possible to make glasses from nonsilicate inorganic compounds. One well-known system is calcium nitrate-potassium nitrate. Also, there is a family of chalcogenide glasses. In my experience people refer to nonsilicate glasses by their generic name, eg nitrate glass, alumina glass, chalcogenide glass rather than "inorganic glass"