What defines a landing gear bogie?
The term bogie initially meant (atleast in Britain) an assembly of wheels forming a pivoted support at either end of a railway coach, which provided flexibility on curves.

So, the term bogie refers to the set of wheels, rotating about the (landing gear) axis, while their arrangement- lateral or longitudinal doesn't matter.

An old patent for Bogie undercarriages for aircraft notes:


  ... a bogie having multiple wheel assemblies mounted on transverse rotational axes spaced one behind the other ...


The issue is that the term has been in use for a long time an has come to mean a number of things (even in railways, the entire carriage can be called a bogie)- so while the correct term is to call it a four (or six) wheel bogie rather than double or triple bogie, it is used quite often. Also, as I already noted, whether it is lateral or longitudinal doesn't matter as long as they are attached to the same (nose or main) gear.