Are "i.e." and "e.g." initialisms?

My trusty Chicago Manual of Style (CMoS), 13th ed. calls e.g. and i.e. "Abbreviations" under the heading of "Scholarship".

Scholarship

14.31 Abbreviations have a very long history of use in the realm of scholarship, and general principles concerning their use are widely agreed upon.

... General abbreviations such as etc., e.g., and i.e. are preferable confined to parenthetical references.

When pronouncing the first, one could say "eye ee", "id est", or "that is."

When pronouncing the second, one could say "ee gee", "exempli gratia", or "for example."

(This AE speaker prefers the English translation of the Latin, but has heard all three pronounced.)

CMoS calls these abbreviations. I suppose if you had to subclassify them, you might call them scholarly abbreviations.