[empath75]

We already have a category for what emoji are: pictographs.

[marxidad]

That's an orthographic category, not a functional category, for which "interjections" comes close. They are also similar to attitudinals in Lojban.

[bane]

Only if they're used in complete isolation (or as a substitution for writing) and not as an annotation device, which is principally how emojis are used.